In most states including California the speeding ticket will stay on your driving record for 3 years and should automatically fall of your driving record after those 3 years have passed.
A speeding ticket will add one point to your driving record and should fall off without doing anything so long as you continue to have a good driving record over those 3 years and don't get anymore speeding tickets.
If you get too many speeding tickets and points on your driving license you could end up losing your drivers license for a long time and even sometimes for life.