There seems to be a bit of confusion about measurements on here sometimes. I try to always post my directions in both North American measures (cups, which goes basically by volume) and in British measurements (generally by weight, not volume).
Here is what a typical measuring cup looks like that I would use to measure out liquids. (these measurements could be in fluid ounces, cups or millimeters.) You just pour in the liquid to the line which is painted on the outside of the glass. These are not the same cups you would use for fats and or other solids like flour and nuts, coconut etc.
These are measuring cups you would use to measure out solids, such as fat, flour, sugar, coconut, nuts, etc. They are squat and mine are made of metal, but you can get them made of plastic as well. You spoon into the cup what you are measuring and level it off at the top with the flat side of a knife.
In the case of fats you must press down to make sure that the cup is completely filled, likewise with brown sugars. With flour, white sugar, coconut, etc. you just spoon in what you are measuring until the cup is filled and then level off the top. They usually come in 1 cup, 1/2 cup, 1/3 cup and 1/4 cup sizes. You can also get 2 cup sized ones.
Over here in the UK we normally measure by weight. We have scales which help us to do that. I am lucky I have a little Salter scale that measures in ounces, grams, etc. I use this for all my solid weights. I use a glass measure for my liquid measurements, which are generally in fluid ounces.
In my recipes you will usually see two sets of measurements. The British ones, or the ones that are meant to be weighed out will be first and the North American measurements will be next to that or at the end in brackets.
For example I might say:
4 ounces of butter (1/2 cup)
This means that the recipe calls for 4 ounces (weighed) of butter, but if you are in North America you can use a solid cup measure to measure out 1/2 cup.
8.5 ounces of plain flour (2 cups)
This would mean that you weigh out 8.5 ounces of the flour, but if you are in North America you could use a solid cup measure to measure out 2 cups.
In the case of a liquid measurement, the recipe might call for
2 ounces of milk (1/4 cup)
In that case you would use a glass beaker to measure it out, here in the UK 2 ounces on the cup or in North American 1/4 cup.
I hope this clears up any confusion!
I have a very good link in my side bar which leads you to the King Arthur Flour cups to weight chart. It's excellent and has most ingredients included.
There is also a very good chart HERE.