I've had a few people ask if it's easy to get a domain name for their blog. If you go through Blogger it's VERY easy. Domain names through Blogger are $10/year. Yes, you can save a few bucks by going through GoDaddy or another registrar, but then you have to link the domain name to the blog yourself. I charge $20 to link the domain name, so what are you saving if you go with a registrar that is a few buck cheaper? Yes, there are tutorials out there to show you how to link it yourself, but if that seems complicated then consider going through Blogger.
To purchase a domain name through Blogger go Basic Settings at your Blogger Dashboard and click on the Add a Custom Domain link I have pointed out below. click images to enlarge
I would advise that while this domain name is being redirected that you do NOT change your password or any kind of ownership of the blog. It only take a few days and people can still access your blog!