You may need to contact the phone company you have your contract with and ask them to send you a new smaller sim for the new phone (but linked to the old phone number of course).
You can cut the card to size, but the plain surface needs to be Rubbed slightly, you can get a Tem Plate as said, you can also get it cut by your local Mobile shop, the charge a £1.00 here, regards charging your phone, you have to charge your phone in any case.