What is the best way to treat dizziness caused by tmj?

Stop chewing. Soft diet, antiinflammatories, ice, dental evaluation. No gum ever again. There is a special mouth guard called an nti device that your dentist can make that is especially helpful.
Treat TMJ. Treat the underlying TMJ problem. True dizziness (spinning) not caused by TMJ. If you have spinning, see a neurologist or ENT doc.
Dizziness. This is not normally associated with tm disorders. This is more likely related to inner-ear disorders and you should consult an ent.Ear.
Dizziness is tricky. Dizziness associated with a tmj/tmd ailment can occur, but is not necessarily a common symptom. I get referrals from ent's quite often, and the equilibrium (balance) may be compromised by a TMJ element. But you should definitely have an ENT examine you first prior to considering TMJ as the main cause.