Hi i host a forum in my hosting now that was expire and now i buy new hosting but i have backup of my forum how i install forum again in same domain with backup
Upload all the files onto the new host, then I would use Big Dump to port into your new database:
http://www.ozerov.de/bigdump/
It's fairly easy, you just need edit your new database's credentials in there, and upload the .php & .sql file to the same location on your site
so let's say website.com/sql/bigdump.php
Then click "Import" from there, and it'll be done pretty fast.
Delete or hide the "sql" folder afterwards.