Howto/Ideas welcome for affiliate/tracking/shopping for a small local website

Is there anyway to realize this using my actual WordPress website (it’s a web-magazine site)

– send my visitors to a new page where I would show a Product of the day special bargain
– they can clic on the image (or on a buy button)
– then… they get to buy this item online, so they would be redirected to another website, landing on this product page.

The question here is how can I follow if there was a real sale done… so that this other website pays me at the end of the week. I need to find a way to do this, or to track the sale. Or other ideas welcome too 🙂

** I am a small regional website, and I want to do this for small regional businesses, so at the moment, neither my site or their site have an affiliate way to do it, i think. ( To be more precise, these regional shops are not on CJ 😉 )