The number of domestic airlines, competition on popular routes and frequent discounting makes flying in the US a relatively inexpensive proposition (though fares can be high on less popular routes). For a country that owes so much to the penetration of railroads and has such a potent railroad mythology, traveling by train in the US can be surprisingly impractical and not always comfortable. Ticket prices vary in value, but the earlier you make a reservation, the cheaper the ticket. Greyhound has an extensive, cheap and efficient bus network, and traveling by bus enables you to meet the 35 other people stuck in America without a car.
America created the ultimate car culture, so don't be surprised by the fact that nearly everyone of legal driving age has a car and uses it at every possible opportunity. Anyone who has seen an American road movie will know that the country's highways are not only nifty ways to cover large distances, they are also rich in mythic resonances. A road trip along Route 66, for example, is no A to B from Chicago to Los Angeles - it's a pilgrimage along America's 'mother road,' closely bound up with the history of America's expansionist West, the Dust Bowl refugees and, of course, the sweet voice of Nat King Cole.
The ubiquity of the automobile often means that local public transportation options are few and far between, but the good news is that Americans tend to be casual with their car keys and far from stingy with their vehicles, so if you're sticking around for a while you may well find wheels easier to borrow than you think. Rental cars are plentiful and relatively cheap, though major agencies require you to be at least 25 years old. Drive-aways are a peculiarly American phenomenon. It's basically a car delivery system that unites cars that need to be delivered over long distances with willing drivers. If a car needs delivering to a place you're prepared to go, you're given insurance, a delivery date and a set of keys, and Bob's yer uncle.
In rural areas, local bus services are often less than adequate. Urban public transportation is generally much better; catching the subway in New York, the El in Chicago and a cable car in San Francisco is as integral a part of the American traveling experience as hopping on a double-decker bus in London. Cycling is an increasingly popular way to travel around small areas, since roads are good, shoulders are wide and cars generally travel at safe speeds. Walking is considered an un-American activity unless it takes place on hiking trails in national parks.