The USCF is the United States Chess Federation. Each state has an affiliate. I believe California is unique in that it has 2 (north and south). Google "California chess association" to find tournaments, clubs, contact info, etc. You'll need to be a USCF member to participate in a rated tournament. You can buy a membership online here:
https://secure2.uschess.org/webstore/member.php
Ok, now for your questions. Your rating doesn't matter. Big tournaments even have unrated sections (but if not you can play in the open section without a rating, no problem). If you've never played in a USCF tournament then you start as unrated (online ratings are ignored). But especially big tournaments will have near beginner level players, so don't think you're not good enough to play, it's not only masters haha 
I've forgotten where in CA, but that state has one of the country's most active clubs, with quick tournaments every week, which is to say, yes, there are events all through the year (as well as several large annual events. I'm guessing the state championship is one such event).
A good first step would be finding a club near you, and visit. Clubs are happy to have new people, and the organizer / TD (tournament director) will be able to answer all your questions. If you visit during a tournament that may be preferable because then you can observe some of the common stuff like what equipment people bring (if any, like board and clocks) where and what time of day they play, all that sort of stuff.
Small clubs that are something like a group of people who play for fun at a coffee shop every week will probably have tournament players too, who can answer any questions you might have. Big clubs, that require dues, have their own room(s) or building, host their own tournaments etc exist in CA (I would guess), but maybe not near you. If a small casual club is near you and a big one is very far away, I'd visit the small one first.
Hi, I'm 19 and I'm interested in expanding my chess knowledge and playing in over the board tournaments. However, I'm unsure about a few things. First, can I play with a such a low rating? Second, where do I find chess tournaments near the San Francisco area? Third, are these tournaments yearly or are there many events I can join throughout the year. If there any other questions I should have let me know because I'm a bit clueless on what else I should know.