How much is a person's daily fat requirement?

It depends on your caloric requirements and the nature of those caloric requirements. I would say a good rule of thumb for most people is to let fats supply the calories for 1/3 of your base metabolic requirement. Then feed extra activities with carbs.

For me that would work out at BMR = 2,056 kcal
from fat (divide BMR by 3) = 685 kcal
grams of fat (kcal divided by 9) = 76g fat

that fat should be a roughly equal spread of saturated, mono & poly-unsaturated fat.

Bear in mind that the way people divide up their diet like this (protein fat carbs) is HIGHLY variable between different trainees, but most people these days are advocating a decent amount of fat (form healthy sources of course!) in the diet. More specifically, low fat diets are being rightly slammed!