Vomiting animals should not be fed initially, if the vomiting persists for more than 24hours you should make an appointment to see your vet. If the vomiting stops then begin to feed small meals frequently after 24 hours.

There is no benefit in starving cats which only have diarrhoea without vomiting.

Initially if you are only dealing with diarrhoea feed your cats normal food if it has been on a stable diet for some time. Fedd small meals more frequently. If the diarrhoea continues I recommend that you do not offer any more of the cat's usual food, but instead give food that is gentle on the stomach and facilitates recovery. It is important that the cat drinks water. 

If the cat vomits or has diarrhoea, the need for fluid increases.

Gastro intestinal diets are available as dry or wet food from your vet or you can make your own. Ask your local vet what diet range they have in stock.

When it comes to kittens and young cats, I recommend a commercial complete food, then you know they are getting everything they need.

But if you want to cook your own diet:

1. Cook white boiled fish, boiled chicken or boiled lean minced meat with low fat level.

2. Give the diet in small portions, a couple of teaspoons at a time at the beginning and give approx. 4-6 times/day or every 2-4 hours the first day.

3. If this goes well, you carefully increase the amount of food offered per meal and reducing the frequency of meals to 3 times a day for the next few days.

Continue giving bland food until the cat's stools are normal and it fully recovers.

When possible, or if a longer period of time on a soft gastrointestinal diet is necessary, you should gradually switch the cat over to a commercially prepared feline gastrointestinal diet - thereby ensuring that your cat gets the right amount of energy, vitamins and minerals.

When the pet's stools have been normal for about a week, you can start to mix in its original food source in to the cat's diet. Complete this food transition gradually over a few days.

In addition to a gastrointestinal diet, may want  to supplement the diet with probiotics which contain live intestinal bacteria. These are available from your vet and at larger pet stores. Give the supplement as directed.

Contact a veterinarian to request an examination of your cat if the cat does not improve. 

it is particularly important to see your vet as soon as possible if vomiting lasts more than one day or diarrhoea last more than 2 or 3 days. You must see a vet as soon as possible if your cat with an upset stomach also appears generally unwell, for instance any evidence of pain or if it becomes lethargic or sleepy.

If the cat completely stops eating - you must contact your vet as soon as possible, as cats cannot tolerate long periods without ingesting food.