You can submit your website to the 3 major search engines, by following these steps:
a) To submit your site to Google: https://www.google.com/webmasters/tools/submit-url
b) To submit your site to Yahoo & Bing: http://www.bing.com/toolbox/submit-site-url
c) It can take anywhere from 1-3 weeks before your website appears on the search engines. It depends on how soon Google, Yahoo, and Bing process your request.