The move consists in 2 steps:

• Step 1 - Move the public html files of the board (these are the files in your board install dir). Either download them to your pc, then upload them again on the new host. In case the url or server path settings change, adapt all board settings to the new url and server path names. The repair_settings.php tool can do most of the work for you automatically.
• Step 2 - Move your db data from the old host to the new host. Use these FAQs for moving your db structure and data: How do I save my SMF board? and How do I restore the database data?