I have a forum at forumotion.com and I wan't to transfer everything to my new mybb forum at wolfnetwork.it.cx. How can I do it?
Contact forumotion and ask them to give you a database backup for starters.
When I have the database, what should I do next?
Make a new database on the new host, import the database to it, and once you've uploaded all your files, assuming you can get a copy from your current host, edit ./inc/config.php to point to the new one.