When you want to shrink a cotton shirt, the key thing is heat. You can shrink white or color shirts with or without lettering on them.
Using the hottest water setting, wash the shirt by itself. For color shirts add one cup of white vinegar to the wash. The vinegar will lock in the color and keep it from bleeding.
After the wash cycle, remove the shirt from the washer. If the shirt has any lettering or images, turn it inside out.
Using the highest heat setting on your dryer, dry the shirt. This will yield a shrunken shirt.