How safe is to give credit card details over phone.?

When I entered the credit card details in teh website ( Veri sign logo is there), it said the verification number entered is not correct. But i I had entered the correct number only. ABout this when I contacted that company, they asked me to call them and they will take the order via telephone. I want to know how safe is this and also in case if anybody takes my card number and purchase any thing, we can locate them by knowing their IP address of the PC. Kindly guide me