I saw a version of this in a recent wilderness first aid class that involved cutting up your shirt with scissors or a knife. It looked slick, but was pretty hard on the shirt! Here are two simple (and easier to remember) methods that don’t require you to cut up your gear.
Method 1 - Elbow in coat hood
If you have a coat with a hood, insert the elbow of the injured arm into the hood, then tie the sleeves snug on your opposite shoulder.
Method 2 - Elbow in coat sleeve
If you have a coat, insert the elbow of the injured arm into the sleeve of your coat, which will bend your elbow and put your hand somewhere on your upper chest. Zip up the coat (probably with the help of a friend) and your arm is secure.
(Bonus points to freak out your friend: Put your right hand inside your jacket, put your right sleeve in your pocket, and use your right hand some creative way - Pretend to have an actively beating “heart”, make it crawl out from the top of your shirt and start going around your neck, etc. Try it in a mirror, it looks amazing. :-)
Method 3 - Extra shirt “necklace”
If you only have one shirt, this works, but if you want your chest to stay covered, you’ll need a second shirt.
Take your extra shirt, put your head all the way through it, and leave it around your neck like a necklace.
Let's assume your right arm is injured. Reach your right arm underneath the sling shirt, insert your hand down the left sleeve, tuck your right elbow into the right sleeve. Finally, tuck the extra fabric around your right elbow. Done!
If you happen to have a safety pin or two (which is a great item to have in your first aid kit, by the way) you can pin the sling shirt to the one you're wearing, so your elbow can’t swing forward.