It all depends what type of worms your cat has. There are many sorts. The most common one is a nematode (roundworm) that gets passed with the bowel motion in a day or two. A tapeworm takes a bit longer and may need a different wormer, check the instructions.
Wormers don't usually kill the worms, it anaesthetises them so they loose their hold on the gut or wherever they live in the animal, so they travel through the digestive system with the normal food. Eggs are not affected so any drenching has to be repeated in one month with nematodes.