There's a report option at the bottom of each posts on the forums. You'll see it right beside the edit tab. As for shoutbox, there used to be a shoutbox report section, but it was removed after becoming an excuse for drama. The best way is probably to contact a staff member you know - preferably an admin, since they can act on it ) with the offending content and they'll take care of it from there.
On threads there is a report button under the signatures. I don't think it's possible to report someone in shoutbox however through forums. But you could take screenshots of shoutbox and show it to a staff member.
Its preferred to be in private but the little report button on the bottom of posts is the fastest way. As for shoutbox offenses and such you can always click the name and report them via the profile as well. But as stated to start private with a staff member (mainly admin+) and the person is the best route to go.
Also, don't forget you can use @OpalBot staff shoutbox (or here) to request the staff's attention to SB. Especially if it's something that needs immediate attention.