It's easier to understand the process under the assumption that the person is innocent.

If someone is arrested for prostitution, they would be fingerprinted, etc (processed), then within 24-48 hours will have an arraignment hearing. At the arraignment, a judge will present charges and the defendant will plea innocent or guilty. The judge will then set bail. The bail amount will be higher than the defendant can pay in the majority of cases (avg $10,000). The defendant will either buy bail bonds or have family help pay.

If not, which is very very likely, the defendant will be held in pre-trial detention, aka Jail. Half a million people are incarcerated because they are unable to pay their bail. This makes up 2/3rds of the prison population. These people are incarcerated because they are poor. Again, they have not been convicted of anything. During this time, it is very likely that the defendant will lose their job and housing.

After pre-trail detention, the defendant will go to trial. Here the police will produce whatever evidence they have in this hypothetical. For the sake of this hypothetical, the police do not fabricate evidence and instead rely on circumstantial evidence and random testimony from people who hate the defendant. This will be presented to the judge, having already been agreed on by the lawyers for the prosecution, state of xyz, and the defendant, public defender (or maybe private attorney). The judge, acting in capacity of the court, (possibly a jury, but more often a judge) will then either convict or acquit and lay out sentencing if applicable.