I don't know if custom zombie maps work with steam. But if you have to non-steam version it's fairly easy.
There are some dedicated sites like ZomMods or ZombieModding which provide you with various custom maps and tutorials to install them.
Also make sure to check out UGX-Mods for more fancy custom maps with nice scripts.
Most of the time you download an executable file (.exe) and all you have to do, is run that file and you're set up!
It definitely isn't illegal, because with CoD World at War, there is a folder and a menu item "Mods" installed with the game. The game is made for mods!
I personally use Tunngle to play custom maps online. This way you don't need an Activision online profile for Call of Duty. In the game, you choose LAN. Tunngle creates a public LAN, so the game thinks you're actually sitting next to 100 players but really, you're just connected to the Call of Duty World at War-Lobby in Tunngle via the Internet.