Don't wait for your domain to expire. When a domain expires, it enters a period of about 90 days during which it can only be renewed for a huge fee, after which it is awarded to backorders or sold at auction, and only returned to the open market at the registrar's discretion.
At any time before expiration, you can easily change your domain's name servers to direct to your new hosting provider or transfer the domain to a new registrar. Consult your current registrar's documentation for this, but both are many magnitudes less of a hassle than losing your domain at auction.
When moving from WordPress.com, you need to install WordPress first as if it were a new site, then import the export file.
With that said though, we typically don't recommend free hosting providers around here, as they often offer crippled servers that prevent WordPress from functioning properly. If you really need a free blog, WordPress.com is still your best option.
