It's a multi-step process, most of which is detailed here: http://codex.wordpress.org/Moving_WordPress
Here are my bullet points, as I've done it a number of times:
1: Backup everything from the original site. Site files, themes, complete DB dump, everything.
2: Install WP on the new server
3: Upload your backups, specifically /wp-content and your DB backup.
4: Complete a search and replace in the DB for your old domain, inserting your new one everywhere needed.
5: Your new site should now be online. Drink a beer.
6: Once the new site looks good, it's time to kill the old one. Take down everything and set up a redirect with htaccess that will bounce any incoming traffic to the new URL (down to the specific post/page).
I know that's short, but that's the bulk of it. Anything specific you needed to know?