The first thing that will happen is you getting cited for performing a petty offense, such as running a red light or not wearing a seat belt while driving. Upon receiving the citation, you will see that it will have a case number, description of your violation, local law codes, the name of the officer, the fine amount and the deadline to pay it. If you feel that the citation was unjust or inaccurate, you take it to court instead of paying the fine. If you choose to do this, you will want to work with a criminal defense attorney and have them help you present your argument to a judge who may or may not void the citation.
Something to keep in mind is that summary offenses are not like misdemeanors or felony crimes when it comes to the criminal justice system. You have fewer rights during the summary process because you have not been charged with something that could deprive your liberty. You will not be able to have a jury trial (though some states may allow for it), and you will not be able to get a free counsel. Even though you will have to pay for a criminal attorney out of pocket, it would be worth it to not only avoid paying a fine, but to help get the citation off your record.