It is very important to keep your cats teeth clean. They can contract gingivitis and have tartar build up. You should brush their teeth at least twice a week. You can purchase an inexpensive cleaning kit at your local pet store. Try and get one that has a finger brush.
Swaddling your cat in a towel or blanket helps keep most cats calm. Placing your cat in front of you on your lap and put your hand over their nose, lifting your cats upper lip without opening their mouth. Check to see if there is anything abnormal. The teeth should be nice and white while the gums should be bubble gum pink. Brush gently around the gums and teeth. Choose a soft baby tooth brush or a finger brush, you can also use a thin wash cloth. Some cat tooth brushes are too hard and can be abrasive to the gums. Brushing your cats teeth should clear up the gingivtis.
The more often you brush your cats teeth, the less likely they will accumulate tartar build up. The build up of tatar has to be removed professionally and can be expensive. Prevention is the best medicine!