The first thing to note about finding your site on the search engines, is that, for a new site, it can take up to a month to be successfully indexed.
To check whether your site is listed in a search engine, type in the name of your site. Although it may not show for your key terms yet, it will show up if you have a unique name which will show at least if it has been added.
After a few weeks, the search engines will start to pick the site up for extra keywords such as your main site terms, but only if the site is correctly optimised. For more details, please read our article on Search Engine Optimisation.