We are not attorneys and do not offer legal advice. If you are facing criminal charges we suggest you talk to a professional attorney.
If you committed a crime in Los Angeles you were probably either incarcerated at the time you committed the crime (if you were caught in the act) or the police suspect you in connection with a crime. If you are incarcerated you will probably be given the chance to bail out (usually by paying a private bail bond agent a fixed fee for guaranteeing your bail in the amount that you flee) or you are released pending a trial.
The police want to gather information about your case - for this reason they will probably either contact you on the phone, come to your house or ask you to come to the police station for questioning. The police researching criminal cases are very busy and some will be nicer than others - in general, however, it is not their job to decide whether you are guilty or innocent. They just want to gather more information to provide to the court (ultimately the DA decides whether to prosecute you or not). Your attorney can give you advice on what you should and shouldn't tell the police.
If the court feels that there is compelling evidence that you committed a crime you will be summoned to court through the mail. Failure to appear in the court carries extremely heavy fines - many ex-inmates that we have interviewed actually did more time for fleeing the state after being ordered to appear in court than they did for their original crime.
Usually the DA will offer you a plea bargain - this is basically the opportunity to plead guilty in return for a lighter sentence. Remember, the state wants you to plead guilty as soon as possible to avoid having to pay for a trial (which is very expensive) - you should consult with an attorney prior to deciding whether to accept a plea bargain. The state will provide you with a public defender if you don't have very much money but you will almost always do better with a private attorney if you can afford it.