You can do quite a lot of it yourself. Here are some tips to get you started:
Have lots of relevant wording on the front (home) page.
Change the site content regularly. Google (and this is the only search engine you need to worry about as it accounts for over 70% of all searches) will downgrade your site if it finds the content does not change - it will consider the site dormant.
Link your site to a Facebook page and if you can stomach it Twitter as well.
More difficult, but perhaps the most valuable, are references to your site on other sites. The references need to be relevant, so if you are selling woolly socks you won't get many points for a reference on a holiday site - but you would on a site about clothing. Many websites will give you a reference if you give them one in return but you need to contact the websites personally; don't send out a shotgun e-mail. It won't get past most spam filters and if it does it will probably be deleted without being read. I must bin at least a dozen a week..
In the old days people would add words to pages as a sort of hidden text and repeat these words many times (e.g. socks, socks, socks...) but Google will mark you down if you do this now. However, the design of your site might allow for keywords to be entered, and these should be used. For example, still on the socks theme, keywords might be: wool, woollen, warm, socks, stocking, stockings, hosiery, natural, British, etc. What you are entering are words people might use in a search string.
Sign up for Google Analytics. It is free and the amount of data it will tell you about your site and the people who view it might alarm you! For example, what sort of browser they are using, the size of the screen they have plus of course which pages they look at and how long they spend looking at them.
You also need to consider how your site is hosted. This is a more complex field and I am not really familar with it but some hosting packages hide the actual content not on your website but somewhere else and there is a sort of divert mechanism to send viewers to it. My first e-commerce site used Actinic Express and this did this - which makes it much harder for search engines to find your site.
Certain packages are also good or bad at SEO. Wordpress claims to optimise SEO and there is an article with some tips here:
http://codex.wordpress.org/Search_Engine_Optimization_for_WordPress This is aimed at Wordpress but most if not all of what is said applies to any website.
Other applications offer different functionality, Weebly is not supposed to be as good as Wordpress for SEO but I think this argument is more for geeks - at the amateur level I suspect it is fine.