Change your URLs and then ask your provider to point the domain. Your site will be down until your host makes the changes. If you have hardcoded links within your posts such as an image linked as OldURL.jpg you will have to do a search and replace to change the OldURL to NewURL.
From Changing the Site URL
On the Settings->General screen in a single site installation of WordPress, there are two fields named "WordPress address (URL)" and "Site address (URL)". These are also known as the "Home" and "Site URL" settings. They are important settings, since they control where WordPress thinks your site is located. They control the display of the URL in the admin section of your page as well as the front end, and are used throughout the WordPress code.
The "Home" setting is the address you want people to type in their browser to reach your WordPress blog.
The "Site URL" setting is the address where your WordPress core files reside.