Use the Central Terminal Parking Structure. If you are going to pick someone up from the airport the quickest and easiest parking is the central LAX parking structure located in the middle of the traffic loop. This structure is accessible from both the upper and lower levels and is ideal for short waits. The first hour is $3 and every 30 minutes afterwards is another $2. There is a $30 maximum fee for every 24 hours. Entrances to the structure generally line up with the terminal numbers, but even if you miss your terminal you can walk through the structure to the appropriate part of the airport.
Take the official LAX shuttle from Lot C for longer waits. This is ideal for picking up passengers whose flights may be delayed or who experience luggage or customs issues. The first two hours are free, as is the shuttle that takes you the block and a half from the parking lot to the airport and back. Each additional two hours cost $1 with a maximum charge of $12 for every 24 hours.
Try out Park One Public Parking. This parking area is also owned by LAX it charges $15.95 per day for uncovered spots. After the first hour they charge $2 for each thirty minutes. This lot is within walking distance of Terminal 1 (Southwest and US Airways) and has a free shuttle service to the rest of the terminals. There is also a daily valet parking rate of $21.95 for uncovered parking spots.
Consider using one of the many privately-owned parking facilities within the immediate area. These facilities charge more than the city or LAX-owned lots, but they are also better lit and offer better security for your vehicle.
Park your car at the Metro Green Line's Aviation Station Park & Ride lot. The only requirement for parking here is that you purchase one Metro Green Line ticket. Once you have purchased a ticket at the automated kiosk you are welcome to board the free shuttle to the airport. There is no daily or weekly limit on the amount of time you are allowed to leave your vehicle in this parking lot. The base Metro fare of $1.50 is all that you are required to pay regardless of the number of days your vehicle is there. The airport shuttle operation is subject to Metro's weekend and holiday scheduling. The security at this location is not comparable to the privately-owned parking lots or even the lots owned by LAX.