You could do this in a few ways.

The easiest would probably be just to take a full cold backup of the database, transfer all the files to the new machine, then re-open the database from the cold backup.

Another way which some might say is easier is to just take a full export of the database, transfer the dump file, then import into the new database.

Depending on requirements you could do it with hot backups and archived logs, or replication, or any number of more complicated procedures.

I would aim for just transferring a full cold backup though. (Assuming once you move the database once, no work will be done on the older one until it's brought back. If they need work they will have to be able to recover it after you bring back the new database).