Basically my friend has started her business, and a website in the same niche is offering to promote the service on their established website.
He is asking for an affiliate link of her. I don't know how this would work though, how would you set up an actual affiliate ID for someone ELSE to promote your own product/service for you, and set it up so it can track payments, ctr's etc. is this something that can be done manually?
Thanks for the help guys 
You will need to use an affiliate tracking system of some kind for this.
You could do something manually with PHP + cookies and/or database stuff but this will require an experienced coder.
You could also use Google Analytics and track payments with it, then look at referrers to find conversion data, though this is not the most reliable course of action (but easy to integrate).
yes, you would need affiliate tracking
it depends what product also is your friend selling. if it's digital or membership based product, it's easy to use a solution like http://digitalaccesspass.com/
superior support to most i've seen and they've been around the block, outlasting their competitors with similar price points
Or you can just use a hasoffers license, place pixels on the checkout page and generate tracking links from it.