There are two means to do that: A softer method and a more drastic one.
The first Method:
Gently press thumb and forefinger together in the area where her upper and under jaw almost meet. You can also test it out on yourself. You'll notice that you can't really help but open your mouth a little although it doesn't hurt a bit. Be careful, though, while doing it on your cat. She is sick and weak already and won't fight against it much - so no reason to use more force than really needed.
With your second hand you should put small pieces of an easy digestible food (poultry for example) on or under her tongue while her mouth is open.
Some cat owners like to draw up mashed cat food into a syringe and squirt it into their cat's mouth. That seems like a good idea at first but if the food comes out with too high pressure it can get into the cat's airways and weak as she is she probably won't be able to cough it up again. Therefore we advice you to not squirt food with a syringe directly in your cat's mouth.
If the first method fails to force feed your cat, you can move on and try the second method.
The second Method:
For this try you need mashed cat food or other sorts of mashed treats your cat likes. A good alternative for example is kitten nurturing milk which is easily digestible and also has a lot of nutrients in it that your cat needs in her condition.
The mashed food or milk should be drawn up into a thin syringe (without a needle, of course). You can purchase syringes in pharmacies usually for a dollar or two.
Gently push the syringe into your cat's mouth. It's important here that you don't head into the usual direction (tongue and throat) but for her cheeks. You can also pull up one of her lips for that. That way you don't have to force her to open her teeth. Pointing towards her cheeks you press out the food with very low pressure.
Usually a cat can't help it but swallow it now.
Make sure you don't give her too much at once. Having her tummy filled up with too much at once can make her throw up everything again!
You can feed her two to three syringes every two hours. If it works she will be strong enough to eat again after a few days.
If your cat throws up all the food you give her, however, no matter how careful you are you should go and see the vet immedietely. Your cat probably has a more serious sickness than you thought at first. Your vet isn't only able to say what your cat's illness is, he can also drip-feed her with important nutrients that will make your cat strong and fit again.
Picture: CC 2.0 by quinn.anya