I got $20 for Easter and I was wondering if Call of Duty: World at War automatically came with custom zombies, or do I have to buy the custom Zombies?
You do not get any custom zombie maps no, however you CAN download them and put them into your game. If I recall correctly as well there are 2 zombie skins that were available in the game itself if you had a certain purchase.
However if you want the entire zombie experience*and you have the money) you will have to buy the Zombie package which costs about 170$ it includes all the zombie stuff from all the CoD games that had zombie modes black ops, World at war etc...
If you want to get the custom zombie maps here https://steamcommunity.com/groups/Imlikingmyzombies
This should give you a head start. Hope that helps :)