This is a complex question. There are lots of ways to get rank - some are free, some cost money.
When they talk about "organic" search, think free and that it takes a bit longer.
If your domain name is new, it will take a bit longer. You need to enable all the good SEO features that Abantecart has. And place entries in all your Meta Tag Keywords: Meta Tag Description: for every product.
Enabling and using SEO Keyword: feature will help also.
Here's a link to some Google insight.
http://www.gstatic.com/ads/learn/en/gettingongoogle.pdfAnd to get ranking (showing up on the first page) if you have a product that lots of people sell is more difficult. What I am saying, if you sell 'candy' and you want to show up on the first page if someone searches for candy, that will take lots of work and probably buying some adwords, etc. This can get to be costly. If you want to rank for 'My candy', replacing My with your store name, then it will rank more quickly.
Getting placement is not easy, quick, or cheap (either takes time or money). But over a period of time, the search engine spiders will find you and if you have enabled all the area I suggested earlier, you will begin to show up.
This is a very, very short reply to a very complex process. There are lots of helpful articles on Google about marketing and getting rank. Just remember that buying adwords can get to be very expensive and not return high results, so my advice is to get more knowledge about SEO before spending any money for adwords
Another Abantecart User!