An arrest, by itself, doesn't begin formal criminal proceedings. Rather, the filing of a document in court is required. In most instances in state court, the document is a "complaint."
Complaints can be either civil or criminal. Civil complaints initiate lawsuits, typically between private parties or a private party and the government. Criminal complaints, on the other hand, are almost always filed by the government. (Some states allow citizens to file criminal complaints or applications for them.)
A state prosecution usually begins after a police officer arrests someone and presents the case to the prosecution. The latter then files a complaint, which charges the defendant with the relevant crime(s). So begins the legal process.
A complaint typically lists: