I agree with trux. You need to find out for certain whether the conviction was a felony or misdomeanor. It can make a difference. One other thing. At one time, California had a program to help felons find truck driving positions. I don't have any idea whom you need to speak with, but I might start with the state employment office.

It isn't your criminal record causing you the most amount of problems, it's your experience.

Got to school and get hired from there.

Lots of decent companies will hire you with a crime provided you have a good driving record, decent work record, and you haven't been in trouble since.