Online payments are one of the biggest concerns for the new vendors. In reality it is something very simple and fast. The affiliate networks automatically manage payments via secure services. You just need to register to network and follow the instructions given by them. If you do not want to join an affiliate network, there are many services, free or not, which allow you to have a safe and reliable payment system. The number one is perhaps PayPal: no registration fee, fast and easy to set up.
Below a list of payment services by credit card: