It's very easy. Leaving the Pleasant Hill Bart station, head East on Treat Blvd. (the main six lane road next to the Bart station), it's a very busy street with a high speed limit, I'd ride on the sidewalk. Turn right on Bancroft and continue on when it changes to Walnut Ave. (you won't know it changed unless you look at the street signs). Walnut ends at a roundabout and a few yards to your right you'll see North Gate Rd. Take North Gate to the top of Mt. Diablo.
You can avoid Treat by riding South three blocks on Oak Rd and turning left (East) on the canal bike trail and follow it to Bancroft. The canal trail runs by a large park on Oak Rd. you can't miss it.