bfc5084,
Wow that's a big question. Bigger than you know.
When you search for it are you searching for "My New Site" or mynewsite.com?
If your site is new with no inbound links it could be in the sandbox.
Sandbox Effect - Wikipedia, the free encyclopedia
If you are searching for "My New Site" the keywords in your site title -
then if your site is not designed right for the search engines it could be buried
on page 385.
Do you know the basics of SEO? Have you done the basics?
Do you have any inbound links? How new is the site?
Exactly how did you search for it. (Use generic words like I did, not your real site name.)