Here are some helpful sources on moving WordPress when your site's domain/url changes:
Moving WP when your domain name or URLs change: http://codex.wordpress.org/Moving_WordPress#When_Your_Domain_Name_or_URLs_Change
Moving WordPress to another server: http://wphacks.com/how-to-moving-wordpress-to-another-server/
Moving WP from local server to live, by Chris Coyier: http://css-tricks.com/video-screencasts/87-moving-up-with-mamp/
The way you actually dump your SQL tables depends on your host. For example, with HostGator (we recommend them and recommend avoiding GoDaddy & Yahoo) you can access PHP MyAdmin through cPanel. with PHP MyAdmin you can dump your sql tables, open them up on your desktop and then use a text editor to find and replace the old file paths with the new paths.