The quickest and easiest way to do this is by adding ?utm-source= to the end of your URLs and using unique values for each affiliate.
E.g. Affiliate 1 will use ?utm-source=John
Affiliate 2 will use ?utm-source=Paul
Affiliate 3 will use ?utm-source=Ben
Then when the website visitors submit any form, they will have the UTM source populated into their contact profile.
The best way to see all of this information is inside a Pipeline, by using flows to create the pipeline items, and using merge fields in the “Create Pipeline Item” to make sure that you and your affiliates can easily see who is responsible for each sale.