Which airport, LAX? I think some of the shuttles around LA will take you to the DL area hotels. I have no idea how much it would cost. You might find it cheaper or even necessary to go back to the airport to catch a shuttle or the Airporter bus to DL area hotels. Cabs are also an option, but are probably pretty pricey from LAX; not so bad from Orange County. Rental cars from LAX are pretty competitive and might be worth your while if you are moving around a bit. However, depending upon where you are staying at DL, you need to factor in the daily parking charges that some hotels charge.
Supershuttle and Prime Time Shuttle are the 2 main shuttle companies. Try their web sites for more info and quotes.