You can link a Paypal account to withdrawl from a bank account only. They need your routing number.
Go to the paypal site and open an account - Follow their instructions.
+1. You *will* have to give Paypal either your credit card number or your bank account information, but they don't give that information to the vendor. Personally I recommend giving them the credit card number; there are clear policies and procedures which protect you if someone abuses your credit card, and the rules regarding Electronic Funds Transfer may not be as clear or complete. (Though my credit union claims that the debit card is actually safer than the credit card... they may be right, but I'm still nervous about it since I "grew up with" credit cards and know their quirks.)