How much fluid should I give my child to rehydrate him after a bout of gastroenteritis?

Get them voiding. If an infant is taking enough fluid to wet a diaper every 4-6 hrs they are hydrated. It is sometimes hard to tell, if their pee is mixed with diarrhea you must rely on their willingness to drink robustly and keep their mouth moist. Modern diapers often pull away moisture so placing square of toilet tissue in the diaper can aleart you that they peed thru it. When in doubt, check with your doctor.
Enough to get pee. The real question is: how do I know my child is well hydrated? You should keep giving fluid until you see a good number of wet diapers, moist mouth, tears, and bright shiny eyes. Your child should be more awake, alert, active. If they are lethargic, not drooling, not making tears with crying, or having significantly decreased urine, then you need to give more fluids or call your doctor immediately.