There are two strategies to build eCommerce into your existing WordPress site. First, you need to figure out if you need a complete eCommerce platform (ie. you need to sell many products, complex products, integration into other systems, etc.). The reason this matters is there are many eCommerce plugins for WordPress with limited functionalities.
They may be sufficient for selling a few products or digital goods, but not running a complete eCommerce site. If you just need a few products, check out the WordPress eCommerce plugins.
To integrate a complete eCommerce platform with Wordpress, you either need to choose a platform that is also built with PHP or at a minimum runs on the Linux/Apache stack. The strategy used to integrate a complete Wordpress site with a full eCommerce platform is to put them on the same domain and let them share a common design. This way, the user can move seamlessly between Wordpress and the eCommerce platform.