Quick Answer
To convert grams to cups without a calculator, you first need a rough gram value for one cup of the ingredient you are using. Then compare your gram amount to that one-cup reference and estimate the nearest fraction of a cup.
For example, if one cup of all-purpose flour is about 125 grams, then 250 grams is about 2 cups, 62 grams is about 1/2 cup, and 95 grams is a little under 3/4 cup. This method works best as a kitchen estimate, not as a replacement for exact weighing in precision baking.