What can I do to cure minor tmj?

See below. Let your lower jaw be at rest and not touch the upper teeth. Also, opening wide to yawn or bite something can aggravate a temporomandibular joint. Aspirin can reduce inflammation in the tmj. An oral splint can help to reduce symptoms.
Night Guard. You can see your dentist and have a professionally fitting night guard fabricated. It should help with your symptoms.
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.
No real cure. Tmj/tmd normally depending on its severity and symptoms, may never really be "cured, " just maintained. If a disk is dislocated or displaced, it may "recapture" on its own, but there can be cycles of good days and bad days. If your problem is an acute one (like a recent injury or minor bite problem, the chances of re-occurrence with proper treatment may be slight compared to a persistent prob.