Quick option: Remain upstairs, exit Terminal-3 near security checkpoint, walk across bridge into parking structure. Walk directly across (straight ahead, no turns) parking structure, cross bridge to Terminal-4 security checkpoint. Total time: 3 minutes between buildings. You'll have to rescreen at T-4 security checkpoint.
You can exit to the roadway and wait for a shuttle bus to T-4, but the drive time is the same and you'll have an unknown wait time for the bus to show up (LA traffic y'know).
Slow option: Approaching Terminal-3 security checkpoint, keep to your far left and follow the wall. You'll end up at top of stairs for shuttle bus to American Eagle Terminal. Change busses at AE's Terminal for ride to T-4. There's a pretty short wait for each bus, but you don't have to re-screen at security.
Personally, I'd take the walk thru the parking structure. Much quicker and security wait isn't anything close to what the news media likes to make it out to be.
*NO CARRIER* -- A Naval Aviator's worst nightmare!