Ice it. Use an ice pack to reduce pain and swelling. Keep the ice on it for 15 minutes a couple of times an hour for the first few hours after smashing it. Don’t keep ice on too long or you can develop frostbite.
Elevate it. Letting your hand dangle at your side after smashing your finger will simply increase swelling and that uncomfortable throbbing. Hold it up to reduce the pressure in there.
Use it. I don’t expect you to start lifting weights with your injured finger, but keep it moving. If you can’t move your finger or if you can’t feel it after a few minutes (you have to give the throbbing time to go away), then you should visit the doctor.
Take a pill. Over-the-counter painkillers can help relieve the constant reminder that you didn’t move quick enough.