They will take you straight to the door of the hotel. Usually there is a coordinator at the blue van stops, with clipboard and radio. Tell them you need a shuttle to Pasadena. They will radio for one to stop or let you know that one is on the way. The shuttles will usually loop around the LAX horseshoe two or three times, looking for more customers, before leaving for their destinations.
Some shuttles take credit cards - check with the driver before leaving the airport.
There is also a bus service from LAX to Pasadena. At LAX, wait for the bus at the overhead RED bus stop signs. The Airport Bus Company has buses that run to other destinations such as Disneyland. If you are staying in a hotel that is not the Hilton, Sheraton or Marriott, there are usually taxis waiting outside the Pasadena Hilton, the main stop for the bus, that can take you to your hotel. Ask the hotel assistant outside the Hilton to call a taxi for you if there are none there.