If I am setting up a site how would I go about ensuring that the person who gives me a credit card number (for instance) is the person who is authorized to use it? Maybe more generally how would I go about reducing the opportunity for fraud and stolen ID usage whether it be for a purchase or system access.
I don't work in this field (online purchases) but I would think that authentication of a user has to be a very hard/tricky endeavor.
I would say just stick with the industry standard methods.
Someone is assumed to have posession of the card if they can supply information which verifies with the card payment gateway. As part of that, for example is the Mastercard/VISA 3D auth scheme which adds a passphrase to online payments.
You could try and go further than this 2-factor authentication with fraud prevention, but the credit card companies have more of a vested interest in it so just follow their lead.
Another common method is the address verification system, used by lots of online vendors.