Tennis Elbow is a soft tissue injury also known as Lateral Epicondylitis.
It's characterized by pain in outer portion of the elbow, and is commonly caused not only by racquet sports but by repetitive motion. (There may be pain and issues with the wrist tendons as well.)
Rest, Ice and Compression (splints or braces) are often recommended during the acute phase.
Sometimes NSAIDs are recommended... some people might even go so far as to receive steroid injections. Heat and massage may help reduce muscular tension and pain... as with most injuries if the injury becomes chronic the longer it takes to heal.
Personally I'd probably recommend MFR techniques to help soften and mobilize the tissues. But others here may offer a different approach.