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Hi,
This FAQ should help.
In reality all you need to do is:
1. Backup your files onto your PC
2. Backup your database (use phpmyadmin or your host's CPanel)
3. Copy your backed up files into your new webspace
4. Restore your backed up database to the new database
5. Edit mainfile.php with the new xoops_root_path, xoops_url and the new databse details (I've replied to your other post).
If you use the "protector" module (if not, why not?) then you will also have to edit the xoops_trust_path (also in mainfile.php).
HTH