Hi whats the best inexpensive way to travel in Los Angeles once I arrive at the airport?
Are you simply asking about transport from the airport? If so, try: Lyft, Wingz, or Uber. All will be cheaper than a taxi. There is also Super Shuttle as Maria mentioned, and the Fly Away bus is dirt cheap, but it will take up more of your time overall, since it makes stops at every terminal.
If you're asking about just traveling around LA, then my personal recommendation is do not rent a car. Everyone will tell you to do this, but what they'll fail to mention is all the nasty traffic you'll deal with and how impossible (and pricey) it can be to park in certain neighborhoods. It is most effective time- and cost-wise to rely on rideshare services and public transit. Yes, there is actually really awesome public transit here (I take it every day!). Download the Transit app to get real-time departures and figure out the best way to get places. Consolidate your sightseeing by neighborhoods to cut down on a lot of back-and-forth from the west to east side, and take a Lyft or Uber whenever you'd rather not do a bus or train. :)
Depending on how far you're headed to from the airport and if you have company, it might be worth it to walk a little outside the airport and get an uber. My friend and I used a shared shuttle service to get to the hotel from the airport and it took about an hour and a half because the shuttle had to drop some people off in between and had to wait to pick people up. It would have been more cost effective for us to take an uber because we could've just split the fare in half and we would've gotten to our destination in about 15 minutes instead of an hour and a half.
Hey Danni, you could also check out Skurt (http://www.skurtapp.com/) as an option. It's a rental car, delivered right to you and you can drop it off when/where you like as well. I haven't tested them out yet, but they seem to be convenient and more cost effective. Have fun in L.A.!
Last year we booked a shuttle and it worked out well. You can get a shared shuttle, which picks you (and some others) up at the airport and drops you off at your hotel. You can also book a shuttle for yourself only, which is a little more expensive, but not much. We used www.supershuttle.com but there are lots of shuttle options. Book online in advance.
Mentioned in this answer: