How do i know i broke my finger or sprained it?

Exam would be best. However, if you can make a full fist without difficulty and then fully extend your hand/fingers in a wide hand you may have minimal injury. If there are bruises appearing around the joints and they are swollen such that you cannot do the previous maneuver, go get evaluated.

The only sure way to know if you've fractured ("broke") your finger is to have an x-ray taken. I concur with the others though that if the alignment is good and your motion is normal or near normal, then careful and close observation is probably all that is required.