Installing is, in theory, simple:
0. Make sure what Steam calls "Source SDK Base" is installed. It will most likely download automatically though. This mod base is included with all Valve Source-based games. For an up to date list, see this page at the Steam store
Note that you can reportedly not
play mods, including ZM, if you have received HL2DM through the ATI promotion. Only bought games come with the Source SDK Base, which you need for mods.
1. Download the newest ZM full installer
, and the patch to the latest version if there is one.
2. Follow the installer's directions. Your Steam installation's "SourceMods" directory should be detected automatically, but you may have to specify it manually if that's not the case.
When the installation is completed successfully, you should end up with a directory called "zombie_master" in your "SourceMods" directory, eg: X:\Steam\steamapps\SourceMods\zombie_master
3. If there is a patch of a newer version than the main installer you downloaded, install/extract it into "SourceMods" as well, overwriting whatever it wants to.
4. Restart Steam, and play. Alternatively, ask more information with regards to the install process here on the forums.