You could spend hours submitting your site to all the various search engines that are available. If that sounds like a good way to spend a day, go for it. However, you don't have to spend a minute doing anything if your website is set up properly. All of the most popular sites (Google, Yahoo, MSN, AltaVista) do it for you. They do offer places where you can submit your site on your own, but if you are new to the internet, your liable to not have any inbound links to your page. No? Well then they won't find you anyway. What you need to do first, once your site is up and running, is find directories to submit to, including:
By listing your site with these companies, they will provide traffic to you. Then, you will have better search engine rankings. Every 2-3 weeks, these search engines go crawling the web, searching for new sites, new pages, and updates to existing pages to see what's out there. They begin with one link in a directory, and don't stop until they run out of links to follow. So if you've got a website that's listed with various directories, the search engines will find it and you don't have to do anything.
Once you've established inbound links, if you don't want to wait, you can submit your sites to the search engines on your own. Just visit each search engine and type in "submit my URL to (search engine name)". The first or second result should be a link to the search engine's submission page, where you can submit your URL for free. This is not guaranteed to be any faster than letting the search engines find you, though, and it doesn't guarantee that your site will be listed among their results.
There are also companies that are willing to do this for you. You can find many free sites where you type in your URL once, and they'll submit it to hundreds of search engines for you at no cost. This is great if you feel safer inputting your own information, but again is totally unnecessary. The internet has become so efficient, that as long as your website is properly optimized to be search engine friendly, it will be found without assistance from you or any other search engine submitter.
How do you properly optimize your site? I'm glad you asked. Keywords are essential. If you sell auto insurance, use phrases that people search for. For example: auto insurance, cheap auto insurance, car insurance. Use these keywords in your text, but only at 1-2% density. That means use them only 5-10 times per 500 words. You can get a much better ranking with quality content, good inbound links, and only four or five mentions of your keyword than you could if you stuffed your article full of keywords to the point that it almost doesn't make sense.
Oh, and by the way, that's against the rules, too. Yes, there are rules for SEO (Search Engine Optimization) and one of them is no keyword stuffing. Google and Yahoo, along with other search engines, want legitimate websites and businesses that have quality content to present their users, not a page full of keywords that doesn't make sense. If you stuff, you'll be banned, and that banishment is usually life-long. So just don't do it.
So how do you submit your site to search engines? The simple answer is: you don't.