Create your own affiliate tracking solution
There are 2 ways to do this. 1 is native to the platform, quick to setup, but doesn't track later visits to the site using the direct url. The second way requires custom code, and a hidden form field, so requires a little more setup, but with longer tracking periods.
Quick & Easy, but no direct link tracking
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.
More involved setup, but better tracking, and supports later visits to the direct URL
First, you will need to create a hidden field inside a form.