To do this, you need to first understand how search engines find sites to put in their search results.
Search engine providers, such as Google, use automated scripts known as 'spiders' that travel the Internet, follow links, and then send information on pages they find back to the search database. These spiders can only find sites that have incoming links (a link on another page that links to your site).
This means that one of the best ways to promote your site to to create links to it on other sites. Create a link on your blog, post it to del.icio.us, put in on your LinkedIn profile, or tell your friends & colleagues about it.
Some search engines also allow you to submit your site manually. Although this is no guarantee that it will make it into search results, it can help. You can submit pages to Google's index here.