Traveling from Sacramento to San Francisco Airport via train, how to transfer from Amtrak to BART?

I need to get from Sacramento to San Francisco Airport by train. I have read that using Capitol Corridor Amtrak then BART is good. Is the best way to do this by taking CC Amtrak to Coliseum / Oak Airport ) then get onto BART? My question is, is it hard to get from CC Amtrak to the BART? Are they physically close? Do I have to walk? Bus? Thanks so much!