The links in the Codex are useful, but I can cut to the chase for you -
On your new host, do a complete clean installation of the same YaBB version you were running on the old host. You didn't mention the version, and that is critical. If the version is "too old', no one here may be able to help you debug, me included. I'll wait judgment on your response. Generally 2.3.1, 2.4 an 2.5AE share most of the same code, and most of the security fixes are in them, and they mostly have up-to-date mod's and anti-spam tools for them.
Make sure everything works, including registration, e-mail for notifications and password changes. Make sure you can post to the General and Test boards that come with a clean install. By default you should be able to attach a file in the test board, see if that works.
Once everything is 'right'. take a YaBB Backup.
IF you had 'mods' installed, now is the right time to reintroduce them. They may well have changed your data structure, and a 'clean board' may not work with your modified data.
When things are copacetic and backed up, its time to restore the 'data only'.
Read this Codex Article
http://www.yabbforum.com/codex/YaBB.pl?num=1190674425Of course, depending on how the backup was made, and restored - you should check file permissions on all the files you upload.
CHMOD:
http://www.yabbforum.com/codex/YaBB.pl?num=1190660838Don't forget to restore yabbfiles/Attachments as well.
Good Luck