I would like to offer e-commerce capabilities to my customers but I still don't understand all of the pieces.

So far this is how it works (I think)

1. You purchase a SSL certificate and allow your clients to use it for their order page or you tell them to buy their own certificate. This is required so that credit card numbers can be transmitted over a secure connection.

2. You inform your customer to setup a merchant account or you could refer them to someone and maybe pickup a referral fee. This is required so that the money can be deposited into your customers bank account.

3. You use shopping cart software to setup the database of all of the items to be sold and the order screen. This is used by your clients customers to make the actual order.

I would like to know what exactly you should be looking for in your shopping cart software? There seem to be a lot of free options out there as well as more expensive ones like a Miva cart.

Any additional clarification on the entire process would be greatly appreciated. I'm finding the entire process a little confusing.

Thank you

I would also recommend using PGP to encrypt orders as well as them going through the secure server.

It will offer your clients much more protection by encrypting their orders as the site visitors clicks submit or place order or whatever.
See pgpi.org I think for details.