Generally you can say that a cat that hasn't eaten for 36 to 40 hours should visit her vet. If your cat's a kitten or also hasn't touched her water, you should go see the vet after 12 hours already!
Usually the vet will give your cat, independent of his diagnosis, an appetizing compound that has an "irresistible" smell for cats.
Cats, however, don't think it's irresistable in quite a lot of cases and will also refuse to eat it. Of course, one reason for a cat to refuse it is that it doesn't only smell like meat, honey and poultry but also like a vet they surely don't like. :)
So how can you make your cat eating again of her free will?
1. Encourage your cat to eat of her free will
Cats are independent creatures who hate being forced to do something. Therefore forcing food into her should be the last of all possibilities and only be used if nothing else helps and your cat is rather weak already.
If your cat doesn't touch her feeding dish on her own you can put her food directly in front of her nose. If somebody brings you chocolates right to your bed you also wouldn't refuse to eat them, right?
Serve your cat's favorite food. All cat's have different tastes and decide on their own which food they like best. After you tried bringing her the usual dry and wet food you might try it with hacked tuna, cooked chicken, fish food (an often unknown favorite), pieces of young cheese and so on. As we said: Every cat is different. Some even like crisps, chocolate and baby food.
See also: Natural Cat Diet (BARF)
Another idea is to give your cat nurturing milk for kittens. This milk is very tasty for your cat, has no lactosis in it and is very substantial.
Please make always sure that her water dish is in direct reach and filled with fresh water. Dehydration is often worse than food deprivation!
2. Grease food around her puss
A well-known and popular method is to grease the cat's mouth with food to make her lick it off. It's a potent method that should be used only if the cat refuses to eat - even if you are holding it directly below her nose.
There is a special nurturing puree that vets as well as some trader sell. This puree is very fine (very expensive) cat food that can be used for this purpose. Cream also works, of course, has a too high fat content, though. Other possibilities are cottage cheese, baby food, liver sausage and so on.
Just mash the chosen food with a spoon's back until it's an almost uniform mash.
It will, of course, work best if your cat has a marked preference for the mashed food.
This method takes a long time because you can only smear half a teaspoon around your cat's mouth each time. You therefore often loose track on how much you fed her already and howw much is to go into her mouth still. That's why you should make small portions before you go feed her. One portion should be around two to three big spoons full.
At the beginning less (and in return more often) is more. Feed your cat once every two hours. Regular ingestion is better in such cases to make the cat's metabolism work better. Small amounts of food are just easier to digest.
PS: In some (extreme) cases cat's have to be force fed. Your vet will surely help you with your situations and will be able to give you helpful suggestions.
Picture: CC 2.0 by Daniel Dionne