Two broad categories of tasks for placing your site in search engines
- Web site optimization
- Search engine optimization

Basically you optimize your web site to run cleaning and fast, optimize it for search engines crawl and index process then submit your web site to search engines.

For more about step-by-step procedure, check out these sites
http://www.submit-it.com/subopt.htm
http://www.apromotionguide.com/

Alternatively, you can hire some one to do it for you. It is relatively inexpensive for the amount of work involved. Here is a good place to place your optimization project for bid. https://www.scriptlance.com/cgi-bin/freelancers/freelancers.cgi

Best wishes.

A new website will take some time before it will show up on any search engine. Your site first needs to be visited by a search robot and indexed, this could take a few day or weeks.

If you haven’t already done so, submit your site to the major search engines.

Also do some research on SEO or search engine optimization. Make sure your site has good content and is visitor/search engine friendly.

Good Luck!