Anyone who's ever owned or looked after a cat knows that at some point you have to do something it doesn't like, like wipe its paws or give it tablets. At this point your affectionate, friendly, soft little pet reveals its other personality as a predator beautifully adapted to kill. The hair stands on end; the body that normally feels like it's made almost entirely of fluff becomes a double handful of writhing sinews; all five sets of needle-sharp pointy ends come out and blood-curdling screams from both parties fill the air.
So you need to know how to restrain it. Standard solutions are scruffing, which can be tricky and even if your grip doesn't slip, risks the apparently subdued animal returning to violent activity as soon as you start doing whatever it was you had to do; and the blanket, which I personally have never found effective. First you have to wrap the cat tightly enough that it can't get any of its limbs out, but gently enough not to hurt it. That's a very narrow window. Then you have to leave the relevant part of the cat outside, which is often easier said than done.
Here's my solution:
Stand behind your cat, and put your hands around either side of her ribcage. Pet her a bit to keep her calm. Decide which side you want to hold the cat on, and move that hand underneath her body. Your thumb and little finger should be extended sideways, behind the front legs. The other three fingers should be extended forwards towards the cat's chin.
Pick the cat up supported by your hand under her ribcage and bring her towards your hip, tucked under your arm with her head a little way in front of you. Your forearm should be nearly horizontal, along her body. Let her back legs dangle free, and gently but firmly press her body between your arm and hip.
Make sure that you are not in a position where any of her legs can reach a table or other surface.
She might cry and struggle, but this position should not be painful or uncomfortable for her and she's only upset because cats don't like being controlled. If it upsets her don't do it unless necessary.
She shouldn't be able to reach you with claws or teeth, but if she struggles a lot you might find it easier if you hold her scuff with your free hand.