BART is a combination of underground, elevated, and at ground level, but all fully grade separated with roads and anything else crossing. It does go under San Francisco Bay and under Market Street in downtown San Francisco, but much of the rest of it is in the open air. For more information on BART, go to www.bart.gov and if once there you click on stations and schedules you will get a map and list of lines to click on to get specific schedules. This is not Europe or Asia, or even New York. Time between trains on any given line can be as long as 20 to 25 minutes off peak and weekends, so the schedule information can be useful.
If you fly into SFO, the airport people mover can take you to the airport BART station. If you come in at the International Terminal, it is easier to walk to the BART station. Trains here are Blue Line, running from Milbrae to Dublin/Pleasanton. You get on it towing toward Dubline/Plesanton. Going from the airport to Richmond, you have to change trains at some point to a Red Line train. These trains run Daly City to Richmond. The map shows the change point as Balboa Park, which is one station in after Daly City. In realilty, you can make the change at any station between Balboa Park and West Oakland. Balboa Park or a station or two thereafter would be better as you are getting on the train at or near the start of its run so it will be less crowded.
If you fly into Oakland, there is an "AirBART Shuttle" bus which takes you between the airport and the BART Colisuem/Oakland Airport Station. At this station you get on an Orange Line train to Richmond. These trains run Freemont - Richmond, so be sure you get on it going in the Richmond direction.
If you have not ridden BART or something like it before, the procedure is this: Buy a ticket from the farecard machine for each person. It is a credit card size paper ticket with a magnetic strip. You then feed it into a slot in the barrier and pick it up and go through, If you have much luggage it is better to either set it over or shove it in front of you and be very close to it going through. Otherwise the gate may close between you and your luggage. Keep the ticket. You will need it to go out where you go through the same process. If you have the right amount on the ticket, the gate going out will keep the ticket. If you have money left over, it will give it back to you. If you have insufficient money on it, it will give it back without letting you through and you must go to an Add Fare machine and at least sufficient money to go through.