check your logs.
if googlebot crawls your site (should happen every few weeks), then your site is indexed with the most popular search engine in the world. It behooves other competing search engines to update their listings as well, whether you submit to them or not, because if they don't update their indices, then they get overlooked.
Once you are listed with google, then all you need to do is try to boost your rating. The best advice for that is to write good and clean code. Use the alt tag to describe images and be sure that your meta tags are written concisely.
Have other sites provide links to your site. Google refers to that as reverse poularity index or something. It means that your site is more popular, and will rank better.
Finally, look at the sites that come up first in your searches and figure out what it is that makes their site better ranked.
There is no exact science to get better rankings because google changes their methods without warning. Also, google et al don't disclose a lot of details about how they keep their indices, so there's a guessing game involved to an extent. I suspect they'll be changing things up a bit soon because it seems that some people have figured how to get more hits to their sites and affiliate sites.