This raccoon is NOT PLEASED in the least. Sorry. Since I have no credit card (and I don't know who has!) I can kiss EF goodbye... 
1) You can get a pre-paid credit card at any gas station, in many supermarkets, online, etc.
2) If you don't have one and you simply refuse to get one, just ask a friend. Yes, you can book with the card of a friend (as made clear in Cheetahs post)
3) Only ONE person per room needs a card as only ONE person books a room for two/three people.
This process is simply required now, since telephone and email booking isn't possible anymore to make booking fair for everyone and actually doable for the hotel.