GoogleBot finds your site in 4 possible ways.

1 Submit your URL to google for crawling, via the "Add URL" form at www.google.com/addurl.html.
2 Google finds your site from another site that is already index so that google sends a spider to find your link
3 Sign up to google webmaster tools , here it verifies your site and submit a sitemap.
4 Redirect an already indexed page to the new page.