I'm running WinXP and Mandriva Linux as a dual boot. But I want to swap Mandriva for Slackware. The thing is I have no idea where to start.

Any suggestions?

Well obtaining slackware CDs would be an excellent 1st step

One way to do it is to format your mandriva partition and install slackware on it:
Once you are in the slack installer you will have a step where you choose on which partitions to install slackware, choose the current linux partition (as usual good practice is to backup the data prior) format it and viola fresh space for slackware!

If you haven't split /home and /usr/local mount points from / then now is a good time to do so, then if you want to reinstall/upgrade again later you won't need to restore all your user config and programs.

Just a note, there may be a much easier method for doing this, I don't know.

You simplify all things with dual boot if you make /boot a separate partition as well 50-10M if you play with multiple kernels.

I don't see any problem of installing Slackware over the exact partition (or partitions) residing by Mandriva. The only possible difference is Mandriva generally uses Grub whereas Slackware defaults to Lilo. However both boot loaders can handle 10 times more systems than just two. I would let the installer to format the partition too.

If a user doesn't create a separate /boot partition he would find his/her kernels in the subdirectory /boot of every Linux he/she installs. To create a separate /boot partition from new actually complicates things.