I just moved the former page at this location that was mostly about the installation of Mandrake 9.0 here. Nonetheless, much of what was there is still here, since it still applies.

First some links for reference:
Inquirer install guide mostly about Mandrake 9.0

Mandrake 9.1 features

Mandrake 9.0 Quick install guide

Disclaimer: in (some parts of) these install comments I discuss things from the point of Mandrake linux, but a lot I describe in the beginning is the advice I'd give to anyone wanting to install any flavour of linux.

Preparations

Harddisk preparation for dual-boot.
As preparations for the linux install, you may want to boot windows and do the following.
(I'm supposing your PC already has some version of windows installed, most likely windows 95/98(SE)/ME.) You may have one or more hard drives in your system, for now I assume you have just one, with one or two partitions. In the case of one partition, all is fine, just run scandisk and defragment that c:\ drive, and we're good to go.
In the case of 2 partitions, after defragmenting the c:\ drive, make an extra directory on it, to which you copy all your important files from d:\ drive. Also, you may want to backup all your personal data (to floppy disk or cd-r(w), this is a good idea in any case). That way, we can actually trash your d:\ partition during the install process and speed things up.

Windows with NTFS partitions (NT, 2000, XP potentially)
Update: as from Mandrake 9.1 the installation / disk partitioning tool will be able to resize NTFS partitions! However, it seems that this can only function well if there is no data in the part that you free up. Some defragmenters put data at the end of a partition, make sure you don´t use one of those. For more info, you will have to surf the web, as I don´t have any ntfs partitions...
At the moment of this writing, most linux tools/distros actually don't manage to work with ntfs partitions with much success,.. to be more precise, writing is considered problematic; many distros don´t enable reading NTFS partition files in the standard set up. Mandrake has support for reading since 9.0, so that's not too bad.

Another hint: once you use a partitioning tool, you should/can only use that tool in the future. Unless, in an extreme case, you do a full rollback of your harddisk, which generally makes you lose all data. (This can be done by restoring an older partitioning table, you need a utility floppy disk from your harddisk manufacturer.)

Before installing
Preparing your system BIOS for the installation of linux.
Go into your BIOS, how to do that is usually shown during the boot process, often by holding the delete-key during the bios checks. Check your motherboard manual for the correct key(s) if you're experiencing problems.
In the BIOS, you want to make sure that you're not overclocking your system (processor, pci-, agp-bus and fsb at standard clockspeed). If you don't know what I'm talking about, I think we may safely assume you're not overclocking your system. Somewhere you can select:
PnP (or: Plug and Play) OS=Yes/No
set that to No.
In the same vain:
Shadow Video Bios = No
Boot virus protection = No
Boot device order: first cd (if you're installing from cd's that is..), then harddisk.
From the Mandrake install guide:
If you want to use a printer locally connected to your machine, make sure that the parallel port mode is set to ECP+EPP (or at least one of them) and not to SPP. If it's not set this way, you will still be able to print, but your printer will not be detected automatically so you will have to configure it by hand.
Also make sure the printer is powered on and properly connected to your machine beforehand.

I'm not aware of more things that may be problematic to a successful linux install or use, please email me if you have more info on general (to all kinds of mobo's) settings that should be set in a certain way to obtain a functional linux system.

The installation itself

Just put the first cd in the tray and reboot the pc; then type enter when you get to the question if you want to install, upgrade or other. (For completeness, yes you can install from the images on a FAT32 (windows) partition, or from a linux partition, or over the network with NFS, or via ftp. But I won't comment on that here.)

I will now just give some tips and explanations on what and how I do things, along with the screenshots I made during the install (just hit F2 to make a screenshot, you can find them later in /root/DrakX-screenshots/ - somehow I managed to miss some picture moments, so this is not complete..). The following parts are in the installation; I've intermittently put my comments, whereever I have tips to spare. By the way, the first thing that is asked is whether you want to install or upgrade; even if you have an older version of Mandrake installed, it is often wise to do an install than an upgrade. People have reported problems with the result in case of an upgrade from some older Mandrake installation. Upgrade should actually not be used, except when you upgrade (or downgrade) your hardware, for instance you put a different monitor (loaner or so) that isn't capable of handling the resolution and frequency of your former one, or if you change your graphics card or so.

Choosing Your Language

License Terms of the Distribution

Keyboard and mouse settings

Installation Type

Security level

Selecting the Mount Points
-you did prepare your partitions as I described above? Good, then you can use diskdrake (the disk partitioning tool) to setup your harddisk for use with Mandrake. In case you've already had a linux system on your machine, you should know most of this, at least enough to adapt your partitioning table to your needs.
So, just reduce the size of your first partition to have enough space for the others.
What used to be your windows c:\ drive is not directly seen; however, you can see something like: hda (as a tabular shaped thing, with another behind it if you happen to have another hard disk, hdb), a colour code and a bar with some colour on it, possibly just one, with text inside it (hda1:/mnt/windows), or if you had 2 windows partitions (in windows called c:\ and d:\ but now known as hda1:/mnt/win_c and hda2 (or 5):/mnt/win_d) (etc if you had more partitions).
In the centre you can select what the system must do with the partition that is selected (with the mousepointer), as in: delete, mount point, resize, etc. Any grey part is unused/free diskspace, click on it and select what you want to make of it: ext3 (or2), swap or fat32 partition. Note that if your hard drive is fully used (no free space) you have to resize the hda1 (win_c, windows c:\ partition) and make it smaller, or delete the second windows partition, so you can then use that free space to create the necessary linux partitions. My advice is to make your partition table look somewhat as follows:
(normally, there is hda1, then hda5,6,7,8 etc, due to certain standards in counting; the primary partition can contain a maximum of 4 partitions, the extended can contain many more logical partitions, hence the second partition can be hda5, since it may well be in the extended partition... so hda5 might also be hda2, depending on if you've made partitions with Partition Magic or another 3rd party partition manager; also, the partition number may not be in order from left to right, i.e. hda1, hda5, hda8, hda9, hda10, hda7,... in this case, at some point, there has most likely been an hda6, which was deleted and then that space was used to make partitions hda8, 9, and 10.... in the example below, I'm referring from beginning of the drive (win_c) to the end, in case of doubt, just check the cylinder definition)

About the swap partition: traditionally 2x the size of your RAM memory, nowadays not necessary to make it so large, if you use your linux system in a way that it really needs 200MB of swap, you're doing such heavy things that a memory upgrade would be in order..

You just divide the remaining space over the last 2 partitions, if you have a 20GB harddisk, you have about 10GB left, so you can do 5GB - 5GB or, if you are certain you are going to use a lot of files both under linux and windows, 3GB for /home and 7GB for /mnt/win_d because you cannot access any linux filesystem when under windows, and under linux you can actually access all fat32 partitions for reading and writing, so you can make a large win_d to be able to pass large files from the linux environment to windows (like ripped cd's or so).
NB: if you have less than 128MB, you may consider putting the swap space as hda5 (meaning: before the / (so called 'root'-partition)), because your system may regularly use the swap space (and the closer to the beginning of the drive, the faster it reads and writes...).
If you're aiming for a triple boot, for instance because you want to do some testing of betas and releasecandidates, or of another linux distro, you can create another ext3 partition, and just have it mounted at /alt or so. Count on 3-5GB for this one.

Important note! If you create new partitions, they must be formatted so that later the operating system (whichever that is) knows the total size. I recently wasted quite a bit of time of a friend of mine for thinking I could bend the will of the digital universe to my liking. Formatting of newly defined partitions is necessary before any system can use the partition.

DrakX asked me if I wanted to use existing partitions, or create new ones. I used my existing partitions, and I was just asked which of the linux specific partitions I wanted to format, preselecting the / partition and offering the other ext3 partitions I have without preselecting them to get formatted. I left the / partition as the only one to be formatted.

Edit: an addition thanks to John Coombes: under windows you can actually have read access to ext2 (3) partitions, more info here. This may especially come in handy for those who use NTFS as their only windows filesystem and want to exchange data from linux to windows.

Choose Packages and Install

- for a more or less complete install, just select basically all general groups on the left, and all environments on the right bottom side. Leave out the server stuff, unless you know you want to play with that. Keep in mind that it's really easy to install anything at a later point with the software installer. If you choose 'individual package selection' you get to hand pick extra packages.

But any stuff you can pick there, you can also install later. BTW, selecting the development packages does not install the kernel-source, so you may want to add that by hand picking, or later with urpmi.

After selecting, sit back and relax, or take a break,... on a Duron 1GHz system, the software packages install took me more than 20 minutes! Oh and you get to change the cds a couple of times.

BTW, people calling Mandrake bloatware are exaggerating (as the smallest harddisk you could buy 2 years ago was already 8GB), if you look carefully you notice that about 1.6GB out of 2.6GB have been selected to get installed; so now you see why I didn´t tell you to make the / partition larger than 5GB...

You get a warning that you have selected to install a number of servers

And then finally the installation can begin.

Don´t pay too much attention to the estimated time that gets calculated; somehow it was way too optimistic for me...
If you choose ´details´ you get to see name of the package that is currently being installed.
(Note that you can also get to see the kernel and other messages by toggling alt-F1, alt-F3, alt-F7. I forgot which one, but you can even get a prompt and look around. How is that for multitasking! :-)

Switching back to the no-details view, you get some pictures about programs and how nice the selection is that Mandrake has made for you, etcetc.

Root Password

Root is the term for the administrator, and with the root password you can ´become root´ and have full control over your system. Make sure you don't forget whatever you choose, (and also: don't make it easy to guess for someone else if you want to make sure no-one can mess with your machine... no actual words, or worse: names). If you do forget it, you can actually go through this installation again without installing anything (choose upgrade, then don't select anything), and just choose another root password. Oh, in that case you do have to create the same users that existed on your system. Or you may revert to the foolproof idea of just writing it down and putting that in a safe place... :-)

Adding a User
Sorry, no screenshots of this at the moment, but anyhow, just enter a username and password. You can reset/change the password for any user if you have the root password. You can keep adding until you have created useraccounts for your whole household and any possibly guests.

Autologin

If you want, you can set up the system so that upon boot, you (well, the user that you choose) automatically get logged on. This is a non-security ´feature´ from some other OS that people are so used to that omission of it in a true unix-like system would make the system seem to be deficient....
I made it look like this:

and got on with things.

Installing boot loader

Can anyone tell me how you are supposed to start your system if you choose ´skip´ here? Anyhow, I just took MBR, since that is the easiest way. A boot floppy is not a bad idea, in case you do a reinstall of windows for instance, but then you can also restore the bootloader on the harddisk if something were to happen to it, by booting with the first CD (CDROM 1), choosing F1 - and booting into rescue-mode (F1 and type 'rescue' [enter], then select "repair bootloader").

Summary

These are screenshots from the second pc I installed Mdk9.1 on, the first one (my own) had the graphics adapter configured at the desired 1600x1200 resolution, and the correct graphics card selected too (gf4ti4200).

Clicking the "configure" buttons right from the item you want to configure takes you to the respective submenu. I just went through them and set things up: country, graphics, printers, ethernet (here you get to select the hostname of your machine), etcetc.

Servers started at boot

For any server that you have installed, you get to tell if you want it started at boot. It is generally a good idea to switch off ftpd, httpd and such servers that you may have installed to play with, but aren't going to use. You can switch them on later, but they do slow down the boot process. If your boot is very slow, it may be because of this; anyway, this screenshot shows the servers that I switched off...

Summary with adjusted settings

The following shots show the settings after configuring all subparts that were applicable for this machine.

Installing Updates from the Internet

Mostly to get security updates. Unless you have a fast internet connection, you may want to skip this step. Also, if you don't have a fast (flatfee continuous) connection, chances are that you're not going to be an easy target anyway (if you're offline, how could they hack your system...) Feel free to use it though.

It's Finished!

Take out the media (cdrom) and reboot.