Make sure you get certified by the county.
Are you in the city of Alameda, or the county of Alameda? Whether, that doesn't matter since it's both in Alameda county, but jobs are tight in Alamedia county due to AMR losing the contract there to Paramedic Plus, and they are accepting applications on their website (operation doesn't start until Nov 2011), and lost it in Santa Clara county to Rural/Metro (operation doesn't start until Jul 2011), but I expect when they come in, jobs might loosen up since I believe both said they are putting new rigs out (+8 for Alco, and +5 for SCC, however, not sure how true is that). IFT companies like Royal Ambulance, WestMed, and NorCal are hiring. From what I hear, NorCal is hiring biannually. I am unsure about WestMed hiring. I applied, but got nada. I called a lot like two month ago, they were hiring. Called about a month or less ago, and they were no longer hiring. Royal is always hiring from I heard from one of their employees, and even on their site, they say they have positions opened. I'd recommend trying them. You are >21 years or equal, right? Otherwise it'll be tough to get a job. Summer jobs like water parks, and Great America, won't open up until... you guessed it... summer.
By the way, you could google EMT jobs bay area too. :\ Oh well, I had answers. You'll probably get more answers if you Google cause there are a lot of difference ambulance companies and EMT positions, volunteering, and stuff like that, more than what I said. Those are just the more known ones.
I wish you luck.