How to Get to Las Vegas
AirplaneFlying is convenient and popular, but not especially environmentally friendly. (Planes use a lot of energy and cause a lot of pollution per passenger-mile traveled.) For that very reason, I stopped flying myself. There's more about this on my Don't Fly page.
If I didn't talk you out of flying, then my #1 tip for getting the cheapest airfare is to use the "flexible dates" feature of the airfare search engine you use. When you insist on traveling on specific days you almost certainly pay more. You'll get the best deal if you just tell the engine where you want to go and then let it tell you which dates are cheapest to fly.
Before you buy your tickets, consider that Vegas hotels are often three times more expensive on the weekends. So it really pays to visit Vegas mid-week if you can.
The best search engines for finding fares are Kayak and Travelocity. (For last-minute fares, Hotwire can sometimes find a better deal.)
The above is a good short summary, but I actually have a whole website about finding cheap airfare.
BusThe U.S. has only one nationwide bus company, Greyhound. But if you're coming from California, you can get a first-class bus for not too much more money. If you buy your tickets on the web, you can get Los Angeles to Vegas on Greyhound for $42 one-way. The standard fare is $57, and a first-class bus like LuxBus is only $60. The trip takes about 6.5 hours. (I know, their website says 5.5 hours, but my trip was 6.5 hours without any traffic congestion.) If you want to sleep on the bus, Greyhound is actually a better deal than LuxBus, because on LuxBus the attendant will regale the passengers with jokes and stories over the soundsystem periodically throughout the trip.
Vegas isn't served by train, but Amtrak (the train company) lets you book a trip to Vegas on their site. They take you on a bus for the last leg of the trip. The closest the train gets to Vegas is Los Angeles or Kingman, AZ, which are 6.5 and 2.5 hours away from Vegas by bus respectively.