Mini-game:
Select Cartman at the character selection screen. Then, press Up, Up, Left, Down, Up, Up on the next screen. A list of mini-games will appear.

Hints

More Mini-games:
Play as Cartman if you want more mini-games. He is the only character that can play the Rodeo and Beefcake mini-games.

Spank The Monkey Mini-game:
In the Spank The Monkey game, notice that the monkey's butts become red when Mr. Mackey hits them, and become redder every time they are hit. If you forget the pattern, watch the order that the butts turn back to normal.

Beefcake Bonus:
Eat every can of Weight Gain 4000 in the Beefcake mini-game to access a hidden animation at the end.

Thanks to Revolution readers Steven Onate!