Online payment is a critical part of any ecommerce solution. This module makes use of the PHP Omnipay payment library, which does a great job of standardising online payments.
This module integrates with the omnipay library via the SilverStripe-Omnipay module. It is automatically required by the shop module, via composer.
This Omnipay presentation gives a general overview to online payments and integrating omnipay with SilverStripe: http://jeremyshipman.com/blog/my-2c-on-omnipay-integrating-with-silverstripe/
Available payment types
There are a number of Omnipay payment drivers that come with omnipay out of the box.
The best way to find additional Omnipay payment drivers is perhaps to do a search on Packagist: https://packagist.org/search/?q=omnipay
Here is a tutorial for setting up PayPal via omnipay.