A third part shopping cart may or may not have online payment handling functionality.
If you are looking for an easily integratable online credit card payment system, my suggestion would be to have a look at using PayPal's.
Paypal have an online payment sytem you can easily integrate, provided you have at least an "intermediate" level of understanding of PHP and html forms, into your website using either their shopping cart or your own.
I have built my own shopping cart but I use Paypal to handle the online transactions of any online stores I build.
Using Paypal you don't have to worry about the security and legal obligations involved with collecting people's credit card details online.
If interested, maybe have a look at Paypal's website and see what they offer: