Yes, I need to track the session ID through the purchase process to link the purchase to the user accounts. How would I do something like that?
On your page, you have a link or widget that, among other parameters, include your account/affiliate ID. Quite frequently, the store provides various tools to generate textual and graphical links for items they list and sell. The link/widget you place in your system has the product ID, your account/affiliate ID, and extra data passed along such as the user ID from your system.
If the user makes a purchase, this is tracked by the store (like GameStop). GameStop provides a page for you to look up various reports. Transactions are handled by the store.
If you need to get the purchase tied to and stored for a user on your system, most online stores usually offers multiple ways to get that information, depending on your needs, your capabilities and the store's capabilities.