You can submit your site to Google using their Add URL service. It normally takes about a month for Google to visit your site and index it into it’s Search database.
Most of the big search engines allow you to submit your site for consideration. Just visit each of them, and search “Add url” or “Submit Url”. They’ll often display a link to how you can list your site within them.
You also want to try submitting your site to any site directories linked to your genre of site.
If you want to speed up your inclusion into Google, you may want to consider using their paid inclusion service AdWords.