How would you tell the difference if you sprained your finger or if you broke your finger?

Xrays. There is no reliable way to tell without obtaining x-rays.
Hard to say. Many times your response to sprains and breaks in the fingers is similar. You should see your doctor for further evaluation. If the finger is swollen and hard to move because of pain, and especially if there is a lot of bruising, you should get an xray.