I've done this many times.
The the Long Beach beach bike path until it ends, go east a few blocks to PCH and basically follow it south. Always stay on the west side of Hwy 5 until Camp Pendleton where you can ride on the base after showing an ID and chatting up the sentry. Continue south on PCH which changes names a few times, but is nevertheless unmistakable.
There are also signs that say "Bike Path" or "Bike Route" or "Pacific Bike Route" the whole way. Its pretty hard to get lost, just keep the ocean on your right. There are lots of cyclists to ask questions. From Long Beach to Del Mar is about 90 miles and takes about 6 hours.