Disclaimer: I've never been arrested, but if I can glean all this from movies and google, it shouldn't be too hard to understand without a direct personal story.
It's pretty standard, they read your rights, interview you for your name and address, take your picture, and then you may be put in jail depending on what you did. They generally cannot keep you over 48 hours without a hearing. If you committed a minor crime against someone in particular, that person will usually be asked whether or not they want to press charges.
That's where things get kind of interesting, because whether or not you're actually tried for the crime depends on whether they want you to be tried. But of course, in the cases of severe felonies, there's not necessarily that option. The victim can elect not to press charges for attempted murder, for example, but some states have it so that if you go that far, the state is the prosecutor because your crime was disturbing its peace in a manner so violent and upsetting that whether the victim is okay with your attempted murder is irrelevant, your behavior is deemed so abhorrent that the act itself was a crime. Though, the longer the police are involved in a felony case, the more likely it is that whether any charges are pressed is more in the authority of the District Attourney than the alleged victim.
If it's serious, or if it's a black kid, they may choose to pursue the case in Juvenile Court, but the standard procedure is they'll just give the kid a warning or stern talking to and release them after everything's said and done. This is referred to as "counsel and release". If they're in the middle of the city (or if they just don't feel like releasing them for whatever reason) they may choose to hold the detainee for the 48 hour period or up until their parents come get them.
Just kidding, I was bullshitting you the whole time. Black kids get tried in adult court.
