Search engine submission is a term that is frankly out of date. You'll see many search engine technical organisations say they offer it - but it has limited value.
In the days when Alta Vista was the premier location for search on the web, web site owners benefited from registering their sites on a regular basis - often 'submitting' the site page by page.
The arrival of technically more advanced systems represented by Inktomi, Google and Ask Jeeves' Teoma soon made submissions much less important. Now they are only really useful for certain directories.
So how do you make your site prominent in the search engines. You offer quality content and that's it. Only trouble is quality content is simply to say - and much more difficult to deliver in practice.
To understand the process by which search engines predomantly work - visit search engine.