That's something we can do for you. In short, we recommend using a trusted affiliate network (such as ShareASale, Pepperjam, Awin, and a few others) to handle all the tracking and affiliate payment services.
Once you join one of the above affiliate networks you will be given some tracking code (or, in some cases a plugin or extension) to place on your site (globally). You will also need to place another code or pixel to "fire" on your confirmation page after an order takes place.
The above code integration allows affiliates to promote your store to their readers and for the network to track them through to the purchase so they can be paid a commission based on the sale.
We've worked with all major affiliate networks. Some are easier than others. Some are more affordable than others. All do basically the same thing: serve as a marketplace for advertisers (retailers) and publishers (affiliates) to meet (and work together), track conversions (sales), and receive payment for driving e-commerce activity.
As for a specific recommendation, it depends largely on what your needs (and budget) are - we can help with finding a great fit for your affiliate program.