I haven't been to many airports to compare LAX with. The only other "large" airport I have been to was PDX, and I'd say it's bigger than PDX, but I find it pretty easy to navigate! There are signs EVERYWHERE!
For the DRE, you will exit the plane and follow the signs to baggage claim. When you exit baggage claim to the outside of the airport, you will see passenger loading areas. Cross into the center "median" area (they call them islands, I think). You will catch the DRE under the green bus sign. There are these green bus signs at every baggage claim area, I think. If you don't see it immediately, walk one way or the other, and you will find it (other colored signs are for other modes of transport, like taxis and rental cars). And make sure to get the big Greyhound-style Disneyland Resort Express, not the little shuttle that says something like "Going to DISNEYLAND? We're EXPRESS!" They are NOT the same thing! There are conflicting reports about if LAX allows the DRE to be decorated; all the DRE busses I have been on to/from LAX are *not* decorated in any Disney fashion--just plain white. They just have a little sign in their front window that says Disneyland Resort Express. I think it took about 20 minutes from unloading to sitting on the island/median last time I went (in Feb). You can't count much on the times listed for DRE pick-up at LAX, in my experience--they drop off everyone first, then come to do the pick-ups, so their time is most dependent on how long it takes to unload everyone.