How can you tell if elbow is broken?

An x-ray. The best way to diagnose a fracture a bone or joint is my getting an x-ray. This coupled with an evaluation by an orthopedic surgeon will establish the diagnosis and determine the treatment plan.
Exam and xray. If you have persistent, severe pain and a sufficient mechnism in which you could have fractured your elbow (such as a fall), then an exam and xray to see if you have fractured your elbow would be strongly encouraged.