Danielle, you're not a dunce- that title is reserved for a select few around here (they know who they are, ha ha).
I've used Cart32 before - roughly $30 a month for them to host your cart - you can use your own product database, or theirs, pretty easy to set up and quite a few configuration options (e.g., gift certificates, shipping discounts, quantity discounts, etc.). I had a few issues with them, but overall they are pretty good.
I'm assuming they'd like to use something a little more professional than pay pal to process their credit cards, so they need to do the following for payment:
As far as the merchant account goes, your client will have to go to their local bank and request a "card not present" account- similar to those that run mail order catalogs use. Your client will need to explain to the bank what they're doing, so the bank can provide them/you with the proper information.
You will need to set them up with a payment processor, such as Verisign. You will then have to marry the three (shopping cart software with Payment Processor with bank info). You will probably need to explain to your client then that everybody is going to want to take a piece of the action- shopping cart charges a little here and there, payment processor charges here and there, and bank charges here and there. Oh and lets not forget the credit card companies- they get a cut too.
There are also services like www.2checkout.com that allow you to bypass several of those steps, but doesn't give you a lot of control over what the payment portion of the site looks like, and other things. And www.propay.com allows you to receive credit card payment w/o the merchant account/payment processor hassle, but it doesn't allow real-time processing as far as I know. These options may be worth looking in to if your client balks at all the fees they will have to pay to do it the "right" way.
hth
-Elizabeth