Technically you should obtain a drivers license within 10 days of moving to the State of California. However, if you are moving from another country you need to get a Social Security Number (SSN) before you can pass your final exam and it will soon be way more than 10 days. Even so, it is a good idea to get the process started asap.
To get a drivers license you go to the local Department of Motor Vehicles - or DMV for short, everything in USA has an acronym or abbreviation - and get the driving handbook. This will tell you the local rules of the road, and when you feel confident that you can memorize most of the facts you can take the theoretical exam. To get to this stage you need to show that you are legally residing in the state - typically by showing your visa. The exam itself is a multiple choice questionnaire answered right in the middle of the DMV office. Your exam fee covers the chance to retake the exam if you don't pass the first time.
Once you have a SSN you can schedule a practical test, typically 10-15 min driving in the DMV neighborhood in the car you bring yourself.
The legal driving age in California is 16 years, but the licenses for minors are provisional and can be revoked by bad behaviors that have nothing to do with driving, like doing graffiti or other misdemeanors.
Minor driving students need to pass the theoretical test, contact a driving school and get two hours on the road before they can get a permit, a reduced license that give them the right to be behind the wheel if a 25+ year old sober license holder is sitting next to them. This way they can train their practical skills before passing the practical exam. Towards this end DMV also distributes a booklet with the best way to structure the instruction so you can check that all required skills have been trained - parallel parking included!
DMV recommends that you drive with your student driver for 50 hours or more before letting them lose in the traffic. Although this sounds like a lot you can still do your 50 hours without ever driving in rain or snow.
Once a minor has a license it is restricted the first year or until the driver turns 18. During this time minors are not allowed to have anybody else in the car, unless the person sitting in the front passenger seat is the "25+ year old sober license holder". Distraction is the main cause of accidents among the new drivers. They are also not allowed to be behind the wheel alone from midnight to 5 in the morning, again unless they have the aforementioned older co-driver present. So no wild parties where junior drives home, at least not the first year. And driving or not driving - junior is not allowed alcohol at all before he or she turns 21.
Although it is very tempting to get you drivers license here if you are an exchange student, most exchange programs prohibit this for minors.
Note that the rules of the road don't apply on private land unless specifically stated. That means that when you drive in the parking lot of a big mall you can't be sure cars don't drive against the arrows or respect the stop lines. Don't ask me, just drive carefully...