If your cat shows any signs of illness or injury, don't panic. You have an excellent ally close at hand: your veterinarian. Have the telephone number and office hours of your vet handy at all times, as well as the contact info and address of an after hours emergency vet clinic.
Your veterinarian can help with a number of potential problems or accidents, including car accidents, poisoning and infections. Call your vet if you're worried about your cat. He or she may be able to give you advice over the phone, or you may have to bring your pet in for a full examination.
If you think your cat needs an anesthetic, don't give her anything to eat or drink. Always phone ahead to let your veterinarian know you're bringing your cat in. The clinic can then prepare for your arrival, and possibly save vital time if your cat is seriously hurt.
You'll need a container of some kind in which to transport your cat. If you don't have a proper cat-carrier (which are quite inexpensive to buy), a strong cardboard box will be fine. Cut or punch some small holes for ventilation, and tie the box firmly. Don't make the common mistake of half-filling the box with cushioning or there won't be enough room for your cat! A few layers of newspaper or an old sweater will keep him/her comfortable.