What is payment gateway integration?

Payment gateways protect credit card details by encrypting sensitive information, such as credit card numbers, to ensure that information is passed securely between the customer and the merchant and also between merchant and the payment processor.

Login / Sign Up with https://developer.paypal.com/
Go to Dashboard -> Sandbox -> Accounts and create test accounts for seller and buyer by selecting Business and Personal respectively.
Login to Sandbox business account and go to My Account -> Profile -> My selling tools
Manage PayPal buttons and copy the button code and paste in your page.
Manage Website preferences and turn on Auto Return and enter Return URL.
Manage Instant payment notifications and select Receive IPN messages (Enabled) and enter Notification URL.

A payment gateway is a merchant service provided by an e-commerce application service provider that authorizes credit card or direct payments processing for e-businesses, online retailers, bricks and clicks, or traditional brick and mortar.