I'm assuming you use the PHPMyAdmin script to back up your SQL databases. You can use the same thing to restore your backups. Just use the import tool of PHPMyAdmin, it will prompt you to upload the file from your home computer, and then it will upload the file and execute it.
I'm not sure what options you used for the backup, but you may want to back up the current data first (just in case), DROP the database you want to restore, CREATE the database you want to restore, then import, or else you could have duplicated data.