How do I make an Under Construction page or keep visitors from viewing my website until it is ready to go public?

By far the most elegant way to do this is to create a temporary homepage, which can be done in a few easy steps.
Create a new page that has your Under Construction design and message and set it as your site homepage. You might want to use a Splash page-layout or hide the menu from visitors to keep them from browsing your site.

You might also want to make sure that search engines don't index your site while you work on it by adding a special robots.txt file to your site.
We've created a ready robots.txt file that will do this. You can download the file here, after which you will have to upload it to your Site Static Files by going to Control Panel > Site Properties > Special Features > Site Static Files while in Admin view.
Don't forget to remove this file when your site goes public!

Using this technique, other pages of the site will still be accessible if the visitor knows the exact URL to these pages.

Alternatively, you could make all or part of the site accessible only with a password or for members of a mailing list by setting a password in the Access Control section of Site Properties or Page Properties respectively.

A combination of the two techniques creates a publicly accessible Under Construction page and gives you full control over who has access to all the other pages of the site.