You can submit your website to each search engine yourself or the company contracted to design it can do this for you, in most cases you don't have to do anything, because search engines (like all other major server sources on the Internet) get continuous updates of all the active domain names in the world and will periodically look at the sites that are attached to them.
As of January 2010, a search engine may have a site cached within 24 hours of the domain name being registered. Another common way to get a site's content cached by a search engine is to get links from other websites, and allow the search engine spiders to follow those links to your site. Many SEO experts will tell you that search engines prefer finding your site this way and whether or not that is true, you get more value from the links coming off other people's sites.
One more important thing to consider if you want to get a website found by Google or any other search engines is that the site should have enough content on the pages to become a resource for its topic. The content has to be readable by a search engine and has to be put on the website in a way that it would be useful for the visitors.
Having a minimum of 250 words on any given page would be very ideal though this is not always possible when you have a large product catalog. You should also keep in mind that search engines classify the content on the page by using reference points like the site's title, paragraph headers, and other usability information. As a whole, the way a site links to its own pages is also a big hint for a search engine, so your website navigation should be easy for people and the robots.
Search engines do not like to be tricked. Since the advent of search, people have found various ways to artificially inflate their search engine rankings with the goal of siphoning traffic for popular searches into dubious offers by using "bait and switch" tactics. Search engines now have multiple ways of spotting tricks designed to inflate rankings, and will take your site out of their index if they believe you are not providing a good user experience.
The most highly ranked websites get there by having trusted pages that are relevant to their topic matter. For example, Wikipedia results will appear for a wide variety of searches. This is not an endorsement of Wikipedia's accuracy, but instead a reflection of the trust that other web users place in the site as a whole. People also commonly link to Wikipedia articles when they are making a reference to a concept or topic. To get your own site to rank in search engines, it pays to become a trusted resource for your topic. When people refer to your site, and link back to your content, search engines take notice and reward you accordingly. By keeping in mind that the stated goal of Google is to "organize the world's information," you can build your site around this principle so it attracts the kind of traffic you are looking to get.
It should also be noted that search engines are looking for original content. If you have a site that just copies other information, even if you have permission, you should not expect to be featured prominently in search engine rankings. Fresh, timely content or reliable reference material is always going to have an edge over stale information. For topics where a search query is likely looking for the latest information, you may even want to update your site on a frequent basis. In the world of search engines, keywords that are relevant to timely topics are considered to be part of the QDF (Query Deserves Freshness) segment of an algorithm