how much is a "cup" ?

A cup is a volume measure, a little more than 236 milliliters, or 16 tablespoons. On-line you can find many sources to convert a volume measure to a weight measure, for example, 1 cup of AP flour is usually listed as 125 grams (4.4 oz) and 1 cup granulated sugar as 200 grams (7.05 oz). One cup of pure water is 237 grams, so you can use that weight to check your liquid measuring cups. NOTE: America's Test Kitchen uses 142 grams/cup for AP flour...depends on how you get the flour into the measuring cup, and how you level it off. Using weight measures for cooking is usually more repeatable, and grams are more accurate than ounces

dry weight (flour) 4 ounces
liquid weight (milk) 8 ounces

8 ounces

Depends on if it's liquid or solid.
There are many conversion charts available (online, cookbook endpapers, printed charts).
Look up by ingredient, or metric to imperial.