There are three types of downloads available:
To use KeeperFX CCP, you only need a Complete version, and your original Dungeon Keeper CD. You may also download the lates patch (if available), but the game should work even without it.
For installation details, see readme file.
Here you can find some variations of KeeperFX.
If you wish to have the really latest version, you can download (in other words, checkout) the current source code from SVN repository. Explanation of how to get the source is here:
To recompile this source, you only need MinGW - install it and type "make all" in your checkout folder. Note that some versions of MinGW have "make.exe" renamed to "mingw32-make.exe" for compatibility; in this case type "mingw32-make all".
If you want a binary build of the code repository, check nightly builds page.
If there's something wrong with the current release, you can try older versions of KeeperFX available here. Still, it is strongly recommended to use the latest version.