Vehicle violation citations can be issued for both moving and non-moving violations, including failure to signal while changing lanes, speeding, parking too far from the curb and overstaying your time allotment in a metered parking space, among others. Most issuing regulatory agencies -- from parking authorities to police departments -- use citation numbers as one way to catalog the citations that have been issued. Most are pre-printed on the front top of a citation but some are on the back. Usually, they are in bold-face type font to make it easier for you to find when you mail in your fine. Some are printed on multiple locations, one that stays with you and another on the stub of the ticket that you mail in with the appropriate fine for your alleged misdeed.
Look closely at the front of the ticket. It will contain all kinds of required information to identify both you (if it is a traffic violation) and, at minimum, the vehicle. The police or parking authority or other issuing agency will check on the license plate and Vehicle Identification Number, usually required to be displayed prominently on the driver's side dashboard (and the engine but for most citations the issuing authority won't go that far initially). Every situation is different. If it is for a parking violation, the license number and state of issuance will show to whom the vehicle belongs. If it's a parking ticket and you didn't park the vehicle, the onus of responsibility still falls on you.
Look closely at the back of the citation if you don't find a pre-printed citation number on the front of the citation. Again, the citation should be pre-printed on the citation upper portion and should be printed on a lower detachable portion on the bottom of the citation that you send back to pay the fine. That's how the issuing agency determines that the fine is paid for a particular infraction.
Some states and municipalities, oddly enough, rely on the representative of the issuing agency to fill in a citation number (presumably in numerical order) but those communities are few and far between. Of the more than half-dozen state police, municipal police and parking authorities contacted from Pennsylvania to California, not one didn't use pre-preprinted citation numbers on their citations. It makes it easier on the issuing agencies to keep their records in order.
Contact the issuing agency if you lost your citation. You will need to know the municipality in which it was issued and the police agency with jurisdiction in that community if the citation was issued for a moving violation. Contact the parking authority, if there is one, in the community in which you may have received a non-moving violation. Many communities don't have parking authorities and rely on local police to issue the citations. Call the city hall, borough or township building to determine if this is the case and then contact the issuing agency. The issuing agency can usually determine the citation and its number (if applicable) from your license plate number.
Pay the fine for the violation in a timely fashion if you don't plan on disputing the citation. The lack of a citation number is not sufficient grounds for the charges to be dismissed. In fact, if there is a citation that has been issued and the number differs than that recorded by police, it can be corrected without prejudice in the case against you, so don't plan on using that as an argument. The complaint can always be amended.