Currently, under California law, possession of less than an ounce of marijuana is the lowest level misdemeanor possible. The maximum possible punishment is a fine of no more than $100, but it is still a misdemeanor.
Governor Schwarzenegger recently signed into law Senate Bill 1449 which will change the classification of possession of less than an ounce of marijuana from a misdemeanor to an infraction. It will still carry the maximum possible fine of $100, but will be classified like other infractions such as speeding tickets.
The law will go into effect January 1, 2011. Until then, you will potentially face misdemeanor charges for your possession case.
Misdemeanor or infraction, you still have rights. There may be legal defenses to your case including challenging the search that lead to the discovery of your marijuana, challenges to your statements under Miranda grounds, etc.