Likely you were cited for driving without a seat belt under 27315(d)(e) of the California Vehicle Code which states the mandatory use of safety belts is required. Subsection h of this part of the California Vehicle Code states:
(h) Any violation of subdivision (d), (e), or (f) is an infraction punishable by a fine of not more than twenty dollars ($20) for a first offense, and a fine of not more than fifty dollars ($50) for each subsequent offense. In lieu of the fine and any penalty assessment or court costs, the court may order that a person convicted of a first offense attend a school for traffic violators or any other court-approved program in which the proper use of safety belts is demonstrated.
The fine listed for a ticket for the 27315 offense on the CA Uniform bail schedule is $76.00. This is for a first offense so as you can tell the $20 penalty grows a bit when you add on court costs, county fees, etc.
If this is your first offense for a seat belt offense you may see if you are allowed to take a traffic school class instead paying the fine, assessment and court costs. In general in the State of California you must not have attended traffic school on a prior citation issued within 18 months of the issue date of your present citation in order to be eligible for traffic school. If you have not taken traffic school in the last 18 months then you may want to see about taking it for this offense and thus keeping it off your record.
If you were cited under a different portion of the California Vehicle Code you can search the laws here to see if it lists what the fine amount will be and also look at the Uniform Bail Schedule for CA.
If you were cited for driving without a seat belt we do not see any DMV points listed for this offense unless instead it was a child that was not properly buckled in than you would receive a point on your CA driving record. California courts and DMV are very serious when children under 16 are not properly secured in a vehicle. If cited for a child passenger seat restraint not being used, drivers may receive one "point count" on their driving record in CA.
Generally, this type of ticket or violation will not cause your insurance premiums to rise. However, there are situations when it might raise your rates if you have a high frequency of being cited for driving without a seat belt since it may appear to an insurance company that you drive regularly without your safety belt on and thus be more of a risk to them for being injured in an accident.
Some carriers may remove discounts for safe driver, which is not technically raising your rates, but the bottom line is that your rates are higher. Keep in mind that each insurance company has their own rating system so to find out how your insurance carrier deals with seat belt violation convictions ask your insurance agent about the company's rating system.