ergophobe - 7:15 pm on Jan 28, 2013 (gmt 0)
What CMS is the hosting company using?
If it's a common open source CMS like Joomla, Drupal or a zillion others, than you can just install it.
If you're at some sort of sitebuilder site with their custom CMS it will be a lot more effort.
In general, though
- log into the shell (command line for your site)
- take a tar archive of all the files
- take a database dump
- move the files to a new host
- upload the new database
- update any database settings (DB name, username, etc will probably change)