They generally charge whatever the cost of the room is onto your card. if you skip out on the bill they are paid in advance. If you show up and pay in cash or with a different card, they credit the card for the charges. It can take up to 5 business days for that credit to appear on your charge. Many motel six style places use this method

Some places dont charge the card at all. They simply check to see if its an active card, and what the available balance is. Then if you skip on the bill, or damage the room they have a way to recoup their money. Many 4 or 5 star places use this method.

You can call in advance and speak to the desk clerk to see which policy that hotel uses. You can also ask that they not put any charges on your card, and they may or may not agree to it.

I used to get so upset when I would travel by car and didnt have a credit card (in my early 20s) I had checks and cash, but no one would let me bunk unless I had a card! I used to spend nights in the car simply because no one would let you in without that card.