X-ray. X-ray is the most reliable way to tell if your finger is broken. Even a finger with the worst swelling, pain, and/or inability to move, might not be broken. Get an x-ray to be sure you'll treat the finger properly for best healing and future function.
Finger trauma. History: was there a significant trauma? Pain: pain at rest and pain with motion. Deformity: does the finger appear badly aligned when fingers are straight? When you make a fist, do the fingers fall into their normal position. Bruising? Of course, the definitive way to determine is to have the finger x-rayed.