How do I transfer my WordPress site to a new host?

I need to move the hosting of a WordPress site from Fat Cow to GoDaddy. The domain name has been transferred to GoDaddy and I have a new hosting account ready to go. But I don’t know how to transfer the site. I am told I need an xml backup (which I think I know how to do through Tools>Export), a database backup (which I don’t know how to do), and a backup of the wp-content folder (don’t know how to do this). I’m in over my head.

In addition, I don’t have access to the account at Fat Cow because someone else set up the hosting there and is unavailable to give me the account information. Is this going to be a problem?

If this is not the type of support you usually provide, please let me know.

The site I’m referring to is I used the Simple Market theme.