How do you move a wordpress.com blog to a new host wicth i will be getting with a new domain name. Old wordpress was exampl.wordpress.com How would i delete that old blog after moving?
Use export feature available under Tools section on Dashboard, thru which you can download the posts from there. Install Wordpress on your own host server and then use Import feature to get all the posts and images over there. You can delete the Wordpress.com from Settings tabs of your Dashboard. Look at the Delete blog option over there. But first of all you should import the content on your own host.
No reason to delete the old blog if it has any traffic. If you want to delete the posts after you have transferred them over, that's fine, but after that, just set up a "We have moved" post with a link to the new blog, and feed your rss into the sidebar so that your traffic may find you.
Does the export and import feature also preserve the theme and plugins? I've made many custom changes to the theme in my blog that I would like to preserve when I move the blog.
Nope. Just the posts and pages. You can't take any features from wordpress.com, to a self hosted wordpress.org blog. When you start the wp.org blog, you have to build it from scratch.
Theme changes will be easy to reproduce. And don't delete the old wordpress site, put a link to new blog