I called a small hotel in Mexico and tried to book a room. They didn't speak English, and I don't speak Spanish that well but I had Google Translate open. Everything went fine until I tried to pay the deposit, and they said they didn't take credit cards. I'm not sure but I think they were saying I would need to use my bank account. I have no idea how that would even work, especially since nobody at my bank speaks Spanish. Does anybody have any idea what they might have been trying to explain to me?
It sounds as if they wanted you to make a direct bank transfer - a "wire" payment directly from your account to theirs. For this you would need some details of their bank account, and to know what reference they expect you to attach to the payment. You may be able to do this via your online banking site (if you have one), or failing that a phone call or in person visit to your bank. Transferring internationally may involve recourse to a system like CHAPS or SWIFT (neither the US nor Mexico participate in the IBAN or SWIFT system though apparently).
Before doing this you should assure yourself that the person you are dealing with does genuinley represent the hotel, and that the hotel does exist. There is normally no consumer protection at all on bank transfers - if the person receiving takes the payment and runs, there is very little you can do to get it back.