Ecommerce site does not need any special method to do SEO, you can do as you do for all sites. But focus on targeted audience.
If you see, the ecommerce website is different from other websites like portfolio, service, and more. So for that you have to use more tricks apart from the SEO on page or off page work. Because on the ecommerce website, there are many pages included with the particular product. So that's why it takes some time to boom your website on the search engines. First a fall, you must complete your on-page as well as off-page work for the website. Then you can run your product on the classified ads sites and ebay website.
This is exactly what I would do at least. You will learn a lot from your competitor (especially the ones came to the top of the page 1)
After getting the analysis results, using Google Analytics. Implement on-site and off-site SEO tactics. The former includes meta-tags, title tags, keyword population and etc. The latter would include blog commenting, forum posting, social bookmarking, profile linking and etc. Hope that helps! Best of luck!
First competition analysis Second keywords Selection according to your competitor Third start optimizing On page Fourth do Off page optimization as much as you can do for keeping your keywords in the first page.