I remember when I started my blog in May 2009, I was crazy about the idea of being able to type something in the Google or yahoo searchbox and see my blog in one of the search results.
Actually, for Google and other search engines to index and display your website as one of a search result, they need to know that the site exists. Though, they have bots that track sites and detect new sites and site-pages, the surest and perhaps quickest is to submit the website to their directories.
You can submit your website to google, yahoo and bing. Also submit your website to as much directories as you can and make links to your website. By making links to your website on other sites, forums or blogs, you increase your chance of being indexed faster and also increases your relative ranking.