Integrate Stripe payment in a campaign from Shortstack.com

I have build a campaign in Shortstack ([login to view URL]) and now I wish to integrate a payment solution on that campaign. I have Stripe and know it can be done with their "checkout" tool. I just dont know how to make the two softwares talk together and how to process the token that Stripe gives me after a purchase. I dont have my own server and the campaign is placed on Shortstacks servers. Shortstack provides a widget for code aswell as Iframe.