All cheats need to be entered at the Main Menu screen.
For every cheat, you will need to keep the left analog stick depressed (pushed down, not pulling the stick down towards you) the entire time you are inputting the cheat code.
Each cheat code is spelled out (e.g. BADBABY for unlocking costumes), and each letter corresponds to a button on the controller. Here's how it breaks down:
A = the A button
B = the B button
X = the X button
Y = the Y button
W = the White button
U = up on the Directional Pad
L = left on the Directional Pad
D = down on the Directional Pad
R = right on the Directional Pad
S = the Start button