It's probably around an hour with no traffic. It's straight down the I-5, so easy directions. There is a train that stops across the freeway from Disneyland (about 15 minute cab ride I think) and goes down the coast to Oceanside. I'm not sure if there is a shuttle, but I would think there would be a bus from the train station to Legoland. I think it'd probably be easier to drive.
There's a link over on the SoCal Theme Park board for kids get in free. Buy online thru the LL site. Must purchase by July 8th. Good til the end of Aug.