When you use the "sale" flow, the payment is executed automatically after the customer confirmed. In some cases you still need to wait with delivery. But the contract is closed, and we care for the payment.
When you use the "authorization" flow, the contract is not closed yet. The payment is only authorized and you need to tell us, that we shall capture the payment now.
You can either use the API solution with POST, or the browser solution with GET. The API endpoint to capture the payment is /payment/<hash>/capture. You need no parameters in addition to your API key.
Example of API solution with POST:
POST /payment/tujevzgobryk3303/capture HTTP/1.1
Content-Type: application/json; charset=utf-8;
The browser solution is very similar, but you need to append the API key to the URL. To capture the above transaction your URL is https://api-testing.secupay-ag.de/payment/tujevzgobryk3303/capture/6801fxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx7ace. This will open a transaction overview, and you can capture the payment with a click on a button.