Although PayPal is a good place to start learning about accepting online payments, because you can set up a PayPal account and work with it would having to pay a setup fee. You might eventually also want to learn about the payment gateway Authorize.net as it is being used by many online merchants to process credit cards.

An overview of how it works and their getting started guide can be found in the links.

With Authorize.net, you can setup simply "Buy Now" or "Donate" buttons. But you can also perform advanced integration using the "Advanced Integration Method" (AIM), "Server Integration Method" (SIM), or "Card Present" (CP) APIs.

If you need payment form to show your merchant’s Web domain or if you need to maintain user sessions throughout the payment process, you need to use AIM as opposed to SIM. Using AIM requires merchant to have SSL. Using SIM does not.

Guide for AIM »
Guide for SIM »

Developer's can request a test account.

Authorize.net sells through its resellers whose fees will differ. ZenCart has partnered with ZenVentures for providing Authorized.net service.

References:
How to integrate Authorize.net AIM with ZenCart