For any type of organic traffic (straight from search engine result pages) you need to target certain keywords.
These keywords are whatever your online store is selling, so if its Wholesale Parsnips, you would want to research and see what are the highest trafficked keywords for that niche.
I believe WordTracker.com is a free tool for this.
Then once you find out your niche keywords, it's about building links and relevancy to boost rankings in google (and others search engines.)
If you plan on focusing on paid search, as opposed to organic traffic, you will need to focus on a PPC campaign or some such other agenda, which would require a sizable budget and risk planning, which is a bit complicated and probably not suited for a free e-commerce site.
Anyways, let me know if you have any success (or failure) with this, hope it helps.