If you buy a domain through WordPress.Com, you own it for a year and you’ll need to renew it every year. You’ll be able to point your domain elsewhere if you want to later as well, but if you’re thinking of doing that anyway, it’s probably easier to just buy it from somewhere like Go Daddy; you get a bit more functionality and it’s a little less hassle later on. http://faq.wordpress.com/2006/11/10/domain-mapping/
If it is possible, who can you contact for help with it? The phone number on the “manage domain” screen through Automattic reaches support who say they can’t help “these kinds of accounts”. I am technologically challenged and I can’t get the domain I bought to redirect to another site. Thank you for any help you can offer.