How do I get a job in special effects?
Internet Filmmakers' FAQ
This response is bent towards live-action as opposed to computer graphics, as that is my background, hope it helps. Since I do not reside in California I can't really give you any practical advice about work in California, however, I can tell you that the best way to jump-start a career in SFX is to work for a company doing FX. However, they probably won't just hire you unless you come highly recommended or have useful skills such as sculpting or fabricating or electronics.
So what do you do? You work for free as a Production Assistant (or gopher). You get a copy of a local company directory for your city (or the city in which you wish to work) and get the contact details for all of the FX companies. You then contact them and tell them that you're looking to break into FX. Don't say that you want a job, just that you want to work in the industry. You'll work for free, do work experience, whatever they want. You'll get plenty of rejections, but it's harder for a company no to a person who will work for nothing. This is the fastest way I know of to break into any field.
However, be aware that egos drive a lot of people in the business. Many people are very protective of their techniques and methods, so they may think you are a "spy" or something, you may run into that type of mentality. Big Tip: Do not pretend you know everything, play dumb and soak up as much info as you can. An FX company doesn't want a person who always thinks they have a better idea or knows a different way of doing something (your idea may actually be better, but you really are not in a position politically to offer it). They want an empty page to work for them that they can train or mould to do things "their" way.
After a while they may decide to pay you something or maybe not, but in the meantime, you have established a "presence" in the "biz". You will meet other people in the biz and they will think you already work at so and so's FX company.
The rest is up to you. Once you are in as a Production Assistant, you can look around at various fields within the FX business and see if you have a place there.
Digital Domain has a FAQ which includes a section for people interested in working in the FX industry which can be viewed at their website. You can also visit the VFX Pro and check out the alt.movies.visual-effects FAQ for additional pointers.