When I was learning to bake, I measured everything in my mother's glass measuring cups. They were intended for liquid, and she didn't have dry ingredient measuring cups. Sugar wasn't too difficult to measure this way -- you could pour it into the cup, give the cup a little shake, and it would settle into place so you could read how much was in there and adjust the amount. Flour, however, was a pain in the neck to measure. You'd have to spoon it into the cup, level it carefully with the tip of the spoon while bending over so that your eye was at the level of the line you were aiming for, and keep shifting bits of it around, hoping you were getting the right amount. Brown sugar has to be packed into the cup for an accurate measure; sometimes you'd pack it down so hard that it would hold the shape of the cup when you were done, and sometimes you just didn't want to put all that energy into it and you'd pack it less firmly.
And then there was shortening. What a mess! My mother's method was probably more accurate than most; she employed the Archimedes Principle. If you needed a quarter of a cup of shortening, you'd take a one-cup measure, put three-quarters of a cup of water into it, and add shortening until the level of the water reached the one cup measure. You'd tip the water out into the sink (holding the shortening in with a spatula or spoon and hoping it wouldn't fall into the sink) and there was your 1/4 c. of shortening -- wet, but accurate. The cup, your hands, the spoon and counter-top were probably all smeared with the stuff. (This method also works for peanut butter.)
For years, I read that weighing was the most accurate way to measure ingredients. It makes sense. If you pack that brown sugar in tightly, you've got more in there than if you don't pack it at all. If your flour is compacted, you've got more in there than if it's sifted and fluffy, and the difference can mean a heavy cake or a light cake. If you like the way a recipe turns out and you want to be able to repeat that success, you need to measure the same way every time -- but if you are using volume (cup) measurements, it's hard to do.
How much does a cup of flour weigh? How about sugar? Is white sugar the same as brown? How tightly packed should the grated carrots for a carrot cake be? How about coconut? Finally, with the publication of Shirley O. Corriher's books "Cookwise" and "Bakewise," I got the information at my fingertips. The books have ingredients and their weights in a chart in the back. The information is also available at several places on-line, including the King Arthur Flour website, and there's a calculator at this site that has more information than you will need in a lifetime.
Just to get you started: a cup of all-purpose flour weighs 4.4 ounces. A cup of white sugar weighs 7 ounces, and a cup of brown about 8 (I say "about" because dark brown sugar weighs more than light brown, but 8 oz. seems to work with either). A cup of butter is 8 oz. Please don't use shortening, but if you must, a cup weighs 6.7 oz. Those carrots? 3.9 oz per cup. Walnuts and pecans are 3.5 oz. per cup. Cocoa (remember to sift it!) is 2.9 oz. per cup, and chocolate chips are 6 oz. per cup. You can keep using those glass measuring cups for liquid -- a cup of milk is a cup of milk, and you can't pack it any tighter! E-mail me if you want a weight measurement that isn't here and that you can't find on-line.
My next post will be on how to weigh ingredients!