To get it to happen regularly (as opposed to just when you do CMD-I), it depends on a few things:
1) What kind of server? (MS, Groupwise, GMail...)
2) What kind of interface (IMAP, POP, etc?)
For IMAP accounts, it should be automatic without doing anything -- any message moved out of the server boxes (inbox, sent, etc) by virtue of deletion or movement to a saved mail folder will get removed from the inbox. If it doesn't work, your server is ignoring the request for some reason. For instance, Groupwise for me does this strange thing where it doesn't immediately delete messages I move out of my inbox, but it crosses them out, and eventually deletes them.
For POP, Preferences -> Accounts -> Click on the account -> Advanced -> check "Remove copy from server..." and select the setting you want. But again, the server may ignore the request (GMail does, for instance).