Zombie games are sub-game modes, meaning you make use of the original game modes such as INF and CTF to create an almost entirely new thing (same thing for "Trenchwar" or TW for short). You can play such games by simply checking out the servers online and joining available zombie servers.
Zombie games always involves lots of zombies being placed in one team, while human players such as us would be in the other team. Simple as that, no other mods needed. Other mods or scripts or maps simply add to gameplay.