Google provides a control panel for website owners which allows you to tell Google about your new website and to control how it appears in Google search results.
To get started, you will need to sign up with Google for Webmasters here https://www.google.com/webmasters/
Having signed up and created your website in Google for Webmasters…

…you will then need to get your verification code and add it to your website.
We will be verifying your dotAdmin site using one of the "Alternate Methods".

The method we shall use will be "HTML tag".

Having obtained our verification code, you can now open and new browser tab or window, and login to your dotAdmin website control panel and choose the "Google" options from the "Settings" menu.

Copy and paste the Google verification HTML tag which Google provided into the "Webmaster Meta Tag" field.

Now hit "Save"
Now return to your Google Webmaster screen and hit "Verify"

Google for Webmasters will report your website as verified, and you can now use Google for Webmasters to manage your website listings in Google.