Search engine submission is quite simple really, the main search engines like Google, Yahoo and MSN will find your site automatically if you have links from other sites already on the search engine. The links here will tell you what they suggest you do.
So we know about the major search engines which will be your biggest providers of traffic for sure, But there are lots more that you can submit to which will lead to greater exposure and more visitors.
A great site to help with all aspects of link building is
Check out their huge list of directories and also they have some really good articles that I recommend you read.
Basically the key to getting into the search engines is Links so this is a subject that you must work at.
Search Engine Optimisation
This is essential for getting good placement in search engines. The best place to start learning about SEO is articles and forums theres loads of info out there.
One point I will make is to not overlook the fact that no matter how well you optimise your site the best way to have consistent high rankings in search engines is by having good content relevant to your keywords. Search engines change their ranking methods regularly and when someone does figure out optimisation techniques they are usually exhausted by lots of people and the search engines simply change techniques. Good content is what the search engines want and if you deliver this means the affects of these changes won't affect you much if at all.
If you decide to let a company optimise your site be sure to ask about the changes to search engines ranking techniques and the long term optimisation of your site.