In our extension, entire business logic is contained within a single app/code/community/Foggyline/Stripe/Model/Payment.php file. We are including the external Stripe library via the require_once dirname(__FILE__).'/../lib/Stripe.php'; statement. Then we are implementing the Stripe_Charge::create API call within the capture method, passing it the customer and credit card information. Since we are using the Stripe PHP library, there is not much of the code we need to write ourselves, so the implementation is pretty short and clean.
If you successfully executed all the previous steps, you should now have a functional payment extension. Although simple, functionality of this extension can be further extended by adding the rest of the methods such as authorize, refund, and cancel. Authorize action is actually already contained within the capture method, but sometimes you might want to first authorize the payment then later manually capture it.