A handful per pig is fine each day. Nutritional content / importance of grass is debatable (a few people say grass is essential!) - but mine have had grass maybe once every year, if that, and they have been perfectly fine. Plenty of vegetable variety and their hay fulfills their grazing needs, if they get fed grass too then that is a bonus. Being put out on the grass is nice for them in other ways, as well as the grazing aspect, but it's not necessary.
Introduce them slowly - give just a little more each day until you reach the amount you want to feed. Bloat/diarrhea is common in piggies who have not been fed grass before (or in a while).