BART charges a distance-based fare. It costs $7.90 from Milpitas and $8.15 from Berryessa/North San José for a one-way trip using a Clipper Card. It costs $0.50 more if you do not use a Clipper Card. It costs less if you are a senior or a person with disabilities.
For information on how much it costs to go to other BART stations, see the fare calculator on BART's website.