What is a good way to relieve elbow pain?

Depends on specifics. One would need to know more about the reason for your pain. The elbow is a tricky joint. If you recently injured the elbow you might have an undiagnosed radial head fracture as an example. If you have compression of your ulnar nerve that would lead to a whole different type of treatment. If you tore a biceps tendon that would have it's own treatment options etc...