If you are defending yourself in a criminal case and can't afford a lawyer, the court will appoint you a free (but probably lousy) lawyer.
If you are fighting a civil case, you had better have a case with which a law firm might sympathize. If you were being treated horribly by a huge corporation or something, for example. Or maybe if you have a case that might bring lots of attention to the law firm. Lots of free advertising. Or one that might get to a very high court (especially the Supreme Court).
In those cases, call around to the largest law firms in your area and explain your situation.
If you are just wanting free help with a typical civil case, good luck. You'll need it!