Okay, so to get to the freeway easiest, have the rental car agency direct you to Century Blvd., then head back toward LAX (probably a right turn). Just make sure you stay in the right most lane, which won't go up the ramp to LAX, but will stay at regular road level. When you hit Sepulveda Blvd (immediately in front of the airport), turn left at the light, stay in the right most lane and after you pass through the tunnel (which is taking you under one of the LAX runways), your lane will veer off to the right. Follow it around the bend back to the left and you'll be on the 105 fwy. Just a short hop ahead on the right is a ramp to the 405 south. Simple, easy... nothing to worry about.
Now, for driving in general... DON'T PANIC! Just remember to breathe. Don't let your concerns freak you out. You'll be fine. Just drive how you drive, keep your eyes open and READ THE SIGNS (many locals haven't figured that simple trick out yet) and get into the lanes the signs tell you you need to be in as soon as they tell you... don't wait until the last minute. It's really not so hard to drive around here. Watch what traffic is doing a few cars ahead of you (and take a look as far ahead as you can see from time to time) and you'll see the brake lights coming on before you need to freak out about it (unless you're stuck behind an SUV, which completely blocks your view). If you see someone coming who looks intent on getting in front of you in a merge situation, just let them in... give them space. Everyone's happy and safe that way. Just call them a name and be done with it.
Really, it's just driving. No need to panic. It's not so horrible, if you don't spend all your time worrying about it before you even get here.
LAX to San Diego is pretty simple... 405 south until it merges onto the 5 South in Irvine, then stay on the 5 all the way down. Easy. You'll be there in 2.5 - 3 hours. Put on AM 1070 or 980 for traffic info and when you're done with that, find some nice, soothing music to listen to and keep calm.
You'll do fine.
