Ok. I have big hips and small shoulders, so I have to pull mine over my head too. I wear two sizes smaller than my measurements indicated. It can be done.
Step 1: Don't panic. Really, stop panicking right now! Your binder will not suffocate you. You will not be stuck in it forever. It's not going to hurt you. You will eventually get it on. Breathe.
Step 2: If the binder is partially on, take it off.
Step 3: If it's a tri-top, fold up the bottom edge about 3 inches all the way around. If it's a double front, fold it up 6-8 inches.
Step 4: Put your arms (only your arms) into the binder. Stick your hands through the arm holes.
Step 5: Raise your arms over your head, holding them as close together as you can (I find that I can make my upper arms almost touch behind my head, but this depends on shoulder flexibility). Let the binder fall as far down your arms as it will go. Try to arrange it so that your head is in the head opening.
Step 6: Pull your arms down to your sides. Use the leverage of your arms to pull the binder down. It will bunch up in a terrifying constricting band right under your armpits.
Step 7: Don't panic. Seriously, stop panicking. If your hands are sweaty, rinse them off and dry them. Relax. It may be uncomfortable, but it's not going to suffocate you, and being shaky or panicky is going to make it harder to finish getting it on. And at this point, you won't be able to get it off until you finish getting it on.
Step 8: Find the bottom edge of your binder. This may be difficult - it really likes to hide - but the folding you did should make it easier. I find it easiest to find the edge under one of my armpits.
Step 9: Pull the edge out all the way around the binder. The more of it you get out, the easier it should be - if you can get the whole front edge out, the back should follow.
Step 10: Pull the edge down to your hips (bottom of ribs for the tri top). If there are wrinkles in the inside layer, just pull the whole thing down more until they smooth out. Make sure it's not all wrinkled or scrunched up in the upper back area.
Step 11: Adjust yourself.