You first need to have Frontpage extensions installed as explained in this article.
Open up Expression Web and create your new web site by clicking File > New > Web Site

Then you need to select the type of web site that you want and design the web site in the way you want.

Next you click file>Publish Site... > Select FrontPage Server Extensions and type in your domain name. Click ok.

Now type in your username and password which is available in the Frontpage Extension section of your control panel.

Now select the page that you want to publish to your site and click the small blue arrow, or you can click Publish Web Site towards the bottom right and Publish the website to the server.

This is an example of what should have happened:

If this is what you see then it was finished correctly and all you have to do is repeat these steps for future Publishing.
If it did not go through then please contact our support team at support@appliedi.net.