All you need is a roll of toilet paper and a roll of duct tape.
This ible illustrates how to make a soft cast for a sprained or broken wrist. it can be altered to accommodate almost any jointed limb. You can use paper towels instead of TP.
Wrap the wrist gently and generously in toilet paper until you have a firm but pliable soft cast. This might take a few dozen wraps. Don't be chintzy. It's only toilet paper.
Wrap the wrist in duct tape. Be sure to wrap around the thumb to help keep the wrist more stationary. Wrap firmly but not so tight that the circulation is affected.*
Don't apply the duct tape to hairy arms or hairy anything! The removal would probably hurt worse than the sprain! This isn't a waxing experiment gone wrong. OTOH... If this person was/is drunk, they deserve it. Go ahead and duct tape away!
Make the sling, simply pull off a long piece of duct tape and apply the sticky side to the bottom of the cast and up the sides. When the underside is taped and the wrist is supported, fold the duct tape in half on itself. Do this on both sides.
Tie it around the neck. Get medical attention.
As suggested by suayres, if a broken bone is implicated or suspected, use sticks (or?) to immobilize and reinforce the soft cast. Add more duct tape as needed to secure them firmly into position.