You need to point your domain name to the WordPress.com name severs, this is done at the registrar where your name was registered.
Then come to your WordPress.com blog and get the domain mapping upgrade and map your WordPress.com blog to the domain name you have registered. That will get your blog to show up when you go to the personal domain name.
Email is separate issue. Go to whoever is your email host and get the A & MX record information required to make their email servers work. The A & MX records are then added in the DNS section.
I just moved a blog from my outside host to WordPress.com and I am still using the same mail servers I have been using for several years and the addresses that I was using before the move still work.
It's a two step process and once I got a bit of help with a format issue things picked up and went. Next move should take 5 min of maybe my time to punch things in, then just wait for the internet to do it's magic ( up to 72 hrs ). My visitors should only notice the Theme is different.