What does a private detective do before and during a court in order to prove someone is guilty with his collected evidence?

Imagine this: a private detective takes a murder case and after some time he thinks he has collected enough evidence to accuse somebody. He then wants to present all the evidence in court to prove that person is guilty. So what does he have to do before and during the court?
Can you give me some information? I am considering putting a “courtroom battle”, in which my detective will try prove his suspect guilty while the suspect and his lawyer try to prove the opposite, into my story. That’s will be where the story climaxes. Will it be possible to use a detail like that?
P.S: my story has an American setting.