Cold symptoms in a cat can be caused by a bacterial infection or a virus. Look for symptoms which may include sniffing, sneezing, a runny nose, pus-like discharge around the eyes, difficulty breathing, and lethargy which can all point to a cold. In rare cases, your cat may also have a cough. Increased humidity will help with your cat's breathing while they're sick. Use a humidifier, if you have one, or confine your cat to a steamy bathroom a few times a day for 10 to 15 minutes at a time.  Some cats may dislike being confined. Many will cry and/or scratch at the door to get out. If your cat does this for longer than 3-5 minutes, don't force them. That can cause stress exacerbating the illness and prolonging recovery. When your cat is sick, you may notice discharge around their eyes, nose and ears. A few times a day, take a damp washcloth and gently wash your cat's face all the while murmuring soothing words. Cats react to the tone in your voice and it may help keep them calm while you do this, unpleasant to them, chore. Use warm water. Make sure the water you use is not extremely hot or cold as this can shock your cat's system. If your cat is sick, it may not want to eat. However, it's important they get the nutrients they need to stay strong during an illness. Cats will often lose their appetite when sick walking away from food they would have happily devoured yesterday. If your cat is not interested in eating, try warming it a little in the microwave for a few minutes. This will create a stronger smell and may entice your cat to eat. You can also try providing your cat with a special, tasty food that it may be more likely to eat. You can also try adding some water to the food to make it easier for the cat to eat. If you have other pets, you may need to separate them. Infections such as these are contagious within the incubation period which can be from between 2-10 days. Your pet is also probably lethargic and will eat slower than normal. Keeping other animals at a distance during feeding time will reduce the chance that they take the sick cat's food before they're finished eating. Make sure fresh, clean water is out at all times. A sick cat needs to keep hydrated. Pay attention to the water bowl and refill and /or clean as necessary.  Adding water to canned food can help keep your cat hydrated. Signs of dehydration include sunken eyes, “tacky” gums, and decreased skin elasticity.

Summary:
Identify the symptoms. Keep your home humid. Clean your cat's face. Encourage your cat to eat. Separate other household pets. Provide plenty of water.