The closest airport is John Wayne Airport (SNA) in Santa Ana, about 15 minutes south. Los Angeles International Airport (LAX) is roughly an hour away depending on traffic — which in LA means it could be much longer. Several shuttle services run between LAX and the Anaheim resort area.
If you are on a budget, you can take public transit from LAX: the G Shuttle to Aviation Station on the Green Line, transfer at Norwalk Station to the 460 bus, which drops you at Disneyland. It takes around two hours but costs a fraction of a cab or rental car.
By car, Anaheim is right off the I-5 freeway, accessible from anywhere in Southern California.