Well, my daughter and I are doing that drive tommorow morning! (12 hours from now!)
The Long Beach Airport is very near the 405... take it south (toward San Diego). Look for the exit for 22 (I think this is the Garden Grove freeway?). After awhile, look for the Harbor exit, and take Harbor north (this exchange is a little goofy, no pun intended!). After going through a retail area then by many hotels, Harbor will take you to the south east corner of the Disney property. A left on Katella Ave takes you toward the Disney Resorts (on your right).
With light traffic, it should take about 20-30 minutes... but what do I know, I'm from Texas!
Good Luck!