I myself would actually use a shopping cart script that is already available. That way credit card info could be stored in a database in an encrypted format. If you have a dedicated server you could also block the sql port so that the database cannot be accessed externally.
Another option would be for him/her to check with their payment processor/merchant account provider. Many merchant account providers already have the ability of accepting credit cards online. It may be a good idea to contact them anyways because if you are going to accept online purchases, they will need to know about it most likely. Accepting online purchases is not the same as accepting purchases at a physical retail location. In most cases fees might be a little more since you would not be performing a card present transaction and there would be slightly higher risk associated with it. If the merchant account provider knows you already perform internet sales, they will sometimes even ask you to sign a contract agreeing that you will not perform internet sales with your POS if it was meant for in person purchases. Merchant account providers like to know what your selling, where your selling it, and how much in sales you plan on doing each month. This is all part of their risk assessment and underwriting. If your business is to risky to them, they may tell you to go find another bank that is willing to deal with higher risk merchants. But since this is only going to be for a magazine I am sure the risk in regards to products being sold would be fine. It may just be a matter of paying some higher fees for processing internet transactions. It all depends on who you have for processing your payments.