Put on a shirt that is inside-out without turning it right-side-out first!
1. Find the collar tag and rotate the collar so that the tag is on the top side. Your head is going to go in here. The tag will go over the back of your head.
2. Stick your head through the collar
3. Roll the shirt over your body, turning it right-side-out as you go
4. Force your arms through the sleeves if they are in fact inside-out.
Protip: practice on a tank top, graduate to short sleeves. Sweaters are hard mode.
I "figured this out" as a little kid and managed to astonish someone recently with this trick. Never fold your clothes properly again!