Very confused

OK. So I installed Zencart. Running nicely.

I also bought a GoDaddy SSL certificate. Can I accept credit cards over my domani? Or do I HAVE to buy a third party Authorize.net merchant account .

If I do go my own way...and I get credit cards. How do I go about charging them (and collecting the money from the user's card). I doubt the cart does that itself.

You have to have a merchant account or payment gateway to process credit cards. Once you have one of those set up with a bank or whatever and connected to your cart, then you can accept cards. When you install one of the payment methods in admin > Modules > Order Totals, the cart will process the cards through your gateway. You need to select modules and accounts that are compatible with each other.

An SSL certificate does nothing for your credit card collections, except to insure that all transactions on your site is encrypted.
In order to accept credit cards over the internet (or anywhere else), you MUST have a business account at your local bank, a merchant account through your bank (high dollar!!) or a 3rd party merchant account provider such as edited, AND an authorized (by Authorize.net) gateway service, such as Authorize.net, or again,edited.
Note: edited provides merchant accounts, and the gateway service, if you need it.
Hopes this helps you understand how it all works. Good luck.

If you have a terminal to process cc payments (as in you have a physical store), you can collect the cc information and process the payments offline otherwise, you need a gateway to process the payment.

I use paypal payments pro for all my CC transactions. You can also activate paypal in your admin panel. I think it's in admin>modules>payments..

you can also choose to have manual CC charges where you are emailed the CC info and you charge it manually with your virtual terminal.