I usually measure veggies by putting chopped up veggies into a measuring cup (I have the set of 3 measuring cups that come in 1, 2, and 4-cup ones, and I use them all depending on how much I make at one time).
However, I found that grabbing chopped veggies with my both hands is approximately 1 cup. So that is handy sometimes when there is no cup around (although it doesn't work for already cooked veggies

).
I make vegetable soups often, and my compromise for not measuring before hand how many cups go into it, is to use 2/3 or 3/4 cup of cooked veggies in place of 1 cup raw.