Figure 1. Water intake at various levels of milk production.
Water makes up 87% of the milk given by a cow, and drinking water satisfies 80 to 90% of a cow's total water needs. So why not give them all they will drink? A lactating cow can consume 20 to 40 gallons per day of fresh water depending on production, as shown in Figure 1.
First, let's look at what a cow needs from a properly designed waterer. Cows like to insert their muzzle 1 to 2 inches into the water with their head inclined at 60 degrees to drink. They need about 95 square inches of surface area to drink from, and can drink 3 to 5 gallons per minute. However, a cow only spends about an hour per day drinking, mostly after eating and milking.
So a waterer needs to provide the correct surface area, at least 3 inches of water depth, be at the correct height, and have a flow rate of 3 to 5 gallons per minute per cow. There also needs to be enough waterers available for a cow to get a drink whenever she wants.
That means in freestall or loose housing waterers should have a large open surface area to drink from, present water 24 to 32 inches above the floor, have a minimum depth of 3 inches, have a capacity of 30 to 50 gallons, and since two or more cows can drink at once it needs a minimum fill rate of 10 gallons per minute. As for how many waterers you need, I don't think you can have too many. The rule of thumb is to provide 3 inches of accessible waterer perimeter per cow in the group, with at least two per group, and placed a maximum of 60 to 80 feet apart.
Also consider installing a water reservoir. A reservoir can help buffer the impact of a large number of cows drinking at once, such as when returning from the parlor or from pasture. By using a reservoir even a medium capacity well can provide for a large number of cows.