This article is from the Credit cards and Consumer Credit FAQ, by firstname.lastname@example.org (Steve Adams) with numerous contributions by others.
"In good faith" is not defined in the law, but in practice it means
that you act like a reasonable person and the merchant is expected
to act reasonable too.
At a minimum you should talk to the merchant's customer service
department and send a follow-up letter. You have to allow the
merchant a reasonable time to respond. What's reasonable? Depends
on circumstances. Enough time for mail to go both ways, plus a
couple of working days.
"In good faith" also means that you act promptly. Don't wait three
months after the charge shows up on your bill to complain that you
never got what you ordered.
Back orders are a frequent problem. If the merchant tells you the
stuff is back ordered, you have the right to cancel the order. (If
it's mail order, they're supposed to give you a postage-paid reply
card for this.) Then you can tell the merchant you don't want to
wait and ask for the charge to be cancelled. This may not happen
the same day, but it should be reasonably prompt. Wait a few days
and call the bank to see if the credit has come through yet.