How can I relieve TMJ jaw pain?

Many ways! This question is very vague. Relieving TMJ pain depends on what's causing the pain, or making a diagnosis. Tmj is not just one disease, but one of many disorders of the jaw joint. Usually common sense things like a soft diet, moist heat, and non-steroidal anti-inflammatory medications like Ibuprofen or Naproxen (aleve) will help with the pain. If not, you may want to see a doctor for evaluation.
See a specialist. Tmj problems don't usually subside on their own. The cause and source of the tmj/tmd pain must be evaluated, along with a super thorough history. A TMJ specialist should be consulted to get the answers that you desire.
A few things. Depends on symptoms, and cause of symptoms. 3 signs of TMJ dysfunction: joint noises, joint pain & limited oral opening. Self treat with soft diet, jaw exercises, massage, heat/cold, OTC pain meds. A splint or physical therapy would be next. Occasionally muscle relaxants, biofeedback. Xrays are done for diagnosis. Surgery usually reserved for serious symptoms not responsive to other treatments.
Diagnose and Treat. The cause of tmj\tmd pain is almost always multi-factorial. There are many conservative treatments including removable appliances, moist heat, soft diet, anti-inflammatory medication, etc. What is most important is that you see a dentist with extensive experience in diagnosing and treating this problem as early treatment will prevent much more serious issues later on.