To give you a idea, a typical flight from Miami to Los Angeles costs around $360 round-trip. A stopping flight is always cheaper and United Airlines is usually the cheaper carrier from Miami to Los Angeles doing 1 stop over. Saying this, do check out Virgin America as they also service this route with a nonstop service to Ft. Lauderdale. It's not quite Miami but Ft. Lauderdale is pretty close and it'll be worth the savings.
American Airlines or Alaska Airlines also do this route..looking at fares now. You can get a round-trip ticket from Miami to Los Angeles for about $360.
Miami to Los Angeles by train if you can, I would suggest taking the train. it's slow (take between 5 and 7 days), however, the trip is very scenic along the way as you will be traveling across 8 states states. The Amtrak sleeper train does around 50 stops in all and costs around $400-$500 one-way.