Originally Posted by SouthArk370Z

Tip:
Including domainName only (see cooltoy's and BettyZ's comments above) will find hits for the rest of the search string on the whole web.

If you use site:domainName (works on all the major search engines), it limits the search to the domainName web site.

Which way is better depends on what you're looking for and how widely you want to search.

Edit: If you use -site:domainName, the search will exclude that web site from the results.