The "Payment Methods" page is pretty straightforward, with two sections.
Active payment. The payment methods currently enabled on your shop. An action button
In the "Payment" page, you can see the following sections:
...
allows you to manage the modules, with the same options that the ones available on the Modules page.
Recommended payment gateways. Depending on your location and shop settings, PrestaShop will show you the available payment methods for your country or the markets you are targeting. You can then choose to add payment methods that are relevant to your customers' expectations.
Installing a Payment Module
Installing a payment module is fundamentally no different from installing a regular module: simply click the "Install" button, and all that is left to do is to configure the module.
You should pay a lot of attention to the settings, and make sure they do point to your address or bank account. Configuring payment modules often means you must first be known by the payment service provider, meaning having an account on their service.
Let's install the "Cash on Delivery" module. Find the module in the list, and click on the "Install" button. PrestaShop will take care of everything, send you to the page with the list of all modules, and notifying you of the result. For instance, if a module needs to be configured before it can work, PrestaShop will display a notification box at the top of the page. In the case of the "Cash on delivery" module, there is nothing to configure.