I'm talking about murderers, Rapists, Traitors, Cowards, Incompetency, theft. How exactly did they go about doing this?
It depends. A vestal virgin who disobeys her vows was being buried alive at the Campus Sceleratus. The Damnatio Memoriae was reserved for the traitors of the state. Their memories and statues were erased from public monuments at Rome. Deserters, Sourcerers and Counterfeiters could be punished by the Damnatio ad Bestias where the prisoner is thrown to be eaten by animals. Crucifixion was reserved for the slaves, pirates and enemies of the state. The best example of this punishment is the crucifixion of Spartacus army. Most notorious traitors were thrown to the Tarpeian rocks. Rape was capital crime and was punished with death. The rape of a female or a male, on the other hand if you raped a slave it could be just property damage.
They used Crucifixion on people who weren't citizens of Rome, so if they aren't citizens and they broke a law, then they will get crucified which is scary.