It will often take 90 days or more for new sites to appear in search engines. Search engines are run by independent companies who decide when and how to add new sites to their databases, if they add a site at all.
You are able to submit your site to most search engines manually, such as at the following pages:
Alternately, you can submit your site to a multiple-submission engine such as www.submitexpress.com.
Each search engine is different, but many (such as Google.com) rank your site based on the number of links that point to your site. One way to increase your ranking is to get more sites to point to yours, ie. by swapping advertising links.
Additionally, there is no one way to get your site ranked as it is often the search engines ever-changing trade secret (google.com changes their algorithm about every 3 months).
Frequent the SEOCHAT website for up-to-date articles written by the SEO gurus who have made a living of doing this from day to day.