Hi Cindy,
Unquestionably, the best method to measure flour is weight, not volume. It gives you more predictable results each time, and it actually measures what you want, which is: how much flour am I using? If you measure using volume, you are only determining how much space the flour you are using was taking up while it was in the measuring cups. That is similar to how much flour you are using, but the differences could certainly cause you trouble.
Even I, who believe that weight is unquestionably better than volume, have given recipes with volume for the flour measurement. Essentially, when I do that, it's because I am being lazy. It takes a little more effort to measure out flour by weight than by volume, because with a measuring cup you could conceivably manage it in two strokes: one to scoop the flour, the other to sweep off the excess. Whereas with weight, you have to keep pouring in flour until it hits the proper amount, and if your scale isn't quick enough, you might overshoot your mark. These aren't terribly difficult trials to get through, but they take a tiny bit more effort. So I'll admit: sometimes I am lazy.
Lazy Cooks Take Heart
Now, if you know what you're doing, and you're familiar at least with the type of food that you're making, then you can get by with some laziness. People talk about baking being much more scientific than other types of cooking, requiring precise measurements and so on, but that's not strictly true. There are variations and tolerances in all of the ingredients, and a whole list of things that are completely not in your control. Humidity, barometric pressure, the precise ratio of glutenin to gliadin in your flour, and so on. If these thing all had to be perfectly controlled, we'd never bake. What we need to do is to get close enough and to know how and when to correct it if it goes wrong.
Why Weight Matters
The difficulty with volume measurements for flour is that they can vary so much more than weight measurements. For any given cup of flour, you could have roughly 30% more or less flour than you expect. It's a huge amount, and if you're making something new, you wouldn't know if you have too much or too little or what. That will make everything else about the recipe much more difficult to control.
Factors that cause variations in volume measurements include how you collect the flour and how the flour was before it was collected. If you keep your flour in a clear plastic container like I do, you can look at how much flour is in there to start with, then shake it up and check again. Chances are, it's going to look like you have quite a bit more flour than you did before. For scooping, there are two major schools of thought: the scoop and sweep, or the spoon. If the recipe that you're following was done by a spooner, and you are a scoop and sweeper, you're not going to end up with the right amount of flour.
Some people describe their measurement method along with their recipe, so you can do a better job with the volume measurements. And if this is a family recipe, and you were taught how to do it by a family member, you probably know the proper method for that recipe.
The great thing about weight measurements is that you ditch all of the ambiguity we discussed in the past three paragraphs. The weight is the weight, plus or minus the resolution of your scale. It's really not that difficult to do, and it'll make your life easier.
Know the Formula
You know how people say that you can't really double recipes for baked goods? That's not entirely true. You can double them, if you weigh your ingredients. Usually you run into troubles doubling a recipe with the volume measurement because all of the error from the main recipe, which was small enough to not bother the recipe all that much, is suddenly doubled as well, and now that causes you trouble.
Of course, if you have a recipe that calls for volume measurements and doesn't have weights, what do you do? Ideally, there would be a conversion factor, but as we've discussed, that would depend a lot on how the person who made the recipe measures. But all is not lost.
Most recipes are based on archetypes. There is an ideal muffin formula and method that all muffins are based upon. Same with cakes, yeast breads, souffles, and so on. If you are concerned about the weight of the ingredients, you can go to the archetype and extrapolate from there. Now, some recipes are deliberately varying from the archetype so that they can be moister or fluffier or something, in which case you're probably going to have to do some experimenting. Since that recipe clearly wasn't as good as it should have been (what with the volume measurements and all), you'd probably have to experiment in any case.
For a good first look at master formulas for a variety of goods, I recommend Michael Ruhlman's excellent book/app Ratio. For similar, but more in-depth sorts of looks into food, you might try a book on professional pastry recipes, which tend to be in baker's percentages and done by weight. For artisan bread recipes with weights, the always-thorough Peter Reinhart has a number of books to work from.
If you're feeling confused or discouraged, take heart. The best end product comes from a great recipe. I find mine on line, in great cookbooks, but mostly, from friends. It's always great to use a recipe that's been "kitchen tested" and that you know you love. The other great thing about using a "shared" recipe is that you can always call your friend if it doesn't turn out just right and find out what the problem was. Remember, cooking and baking is NOT brain surgery. Don't take it too seriously, just start with a good recipe, pay attention, follow the instructions and have fun.