If the only thing you're changing is the domain name. ie not the hosting, database or anything it's easy.
1) Backup your database
ACP > Maintenance (tab) > Backup (leftnav)
Do a full backup and download it
2) Disable your board
ACP > General (tab) > Board Settings (leftnav) > Disable Board
3) Change your domain settings
ACP > General (tab) > Server Settings (leftnav) > Server URL settings
Change these to match your new domain.
4) Change your domain how ever your host sets it
5) Change your cookie settings to match your domain
ACP > General (tab) > Cookie Settings
6) Re-enable your board
7) Probably Tell everyone it's changed
tab is a tab at the top of the ACP
leftnav is the Navigation bar on the left