You're using IMAP, correct? The way you do it in Opera is to use the you@example.com IMAP folder access point for the account in the mail panel. You drag the message (or selection) from the IMAP folder it's in to the IMAP folder you want to move it to. If you want to copy instead of move, you ctrl + drag.
But, you can use cut/copy and paste (via the right-click on message/selection or ctrl + x / ctrl + c and ctrl + v) to do the same.
It basically works how you copy/move files in Windows Explorer. Note though that when moving a file from an IMAP folder in one account to an IMAP folder in another account, Opera will force a copy action instead of a move (causing you to have to delete the original if you actually want to move).
There's no move to / copy to option option though and no button for it. Try using dragging or the keyboard shortcuts for a while to see if you like it.
If you're going to be working for IMAP folders, you can drag the you@example.com IMAP folder access point to the top of the mail panel and use that list and ignore the All Messages access point etc. It's up to you.