Los Angeles is both a city and a county, and people often say Los Angeles or LA when they mean the greater Los Angeles area. LA is a huge, but funny-shaped, city. You could start in one end of LA and drive for two hours in one direction without leaving the city limits, and yet there are neighborhoods very near LA that are separate cities. There is very little rhyme or reason to what's part of the city of LA and what isn't. For example, Hollywood isn't actually its own city, it's all part of LA, but most of the beaches are in other cities, like Santa Monica or Malibu. Confusing enough? For the purpose of this guide, we'll be considering all interesting destinations that are within the greater LA area, even though they might not be in the city or county of LA.
LA has five large airports. The 'Ontario' airport out way east of LA, (the site of the fire, circa fall 2003), the Long Beach Airport, the Burbank Airport, the Orange County/John Wayne Airport and LAX. Flying into either the Long Beach, Burbank, Orange County/John Wayne Airport or Ontario airport will save a lot of hassle because they are small and not as busy, but you will typically be farther away from your destination which will entail a lot of driving. Then again going anywhere in LA is going to cost you a lot of driving. If you're going to Disneyland or any of the Orange County beaches (Laguna, Huntington), consider the Orange County / John Wayne airport.
The Greyhound bus terminal in Union Station is loaded with people full of stories about how they need money. To avoid these people, stay inside the terminal, in the middle of it. Dont sit near the edges of the terminal where the doors are, neither out in the front nor near the back where the busses parking spots are. The people will sneak in these doors and ask you for money. The problem with staying away from the edges of the terminal is that the air is filthy. their ventilation sucks. The LA bus stop is down the street from the greyhound terminal exit. You may want to ask for directions before leaving the Grayhound station.
The subway system is cool. As of 2002 it works on a 'trust' system, you buy your tickets from machines, then get on and ride... no checking, no gates, no nothing. you can get maps of this online too and many of them dump out near bus stops. It's called the Metro, and it's actually only a subway in a few parts of downtown L.A. - the rest of the time it's above-ground light rail.
The truth is that Los Angeles is huge and completely decentralized, so the Metro (subway) is only helpful if it happens to go where you want to go. All of the Metro lines meet in downtown L.A., but that's not all that useful since there's not all that much to do downtown. Most of the interesting parts of town, especially on evenings and weekends, are pretty far from downtown, such as Hollywood, Westwood, the Grove, Santa Monica, Venice Beach, etc.
Get a car. Yes, traffic sucks, but if you want to experience L.A., you need to get a car, because some of the most interesting parts of town are very hard to reach via public transportation.
There is a real nice hostel in Hollywood on Orange Street. But be sure to lock the door or the lady will get mad at you.
As Los Angeles is similar to many other major metropolitan areas travel to and within certain parts of the city should be avoided unless absolutely necessary or you know how to handle yourself in a tight circumstance. Homeless and other disenfranchised individuals are a common site in many parts of the greater Los Angeles metro area including but certainly not limited to Downtown(Los Angeles). Most of these individuals are harmless and if you are asked for money a polite refusal will typically send them on their way.