Question

How is the amount of urine produced regulated?

Answer 1

This depends on the secretion of antidiuretic hormone  ADH ...
If there is large amount of water present in your body then ADH production decreases and rate of urination increases so that extra water can be removed...
if you are dehydrated then ADH secretion increases so that you can preserve more water in your body hence amount of urine decreases.... 

Answer 2

Antidiuretic hormone (ADH) is produced by the hypothalamus and stored in the posterior lobe of the pituitary gland. Its function is to make membrane in collecting ducts permeable to water. it is released in response to a decrease in H2O, decrease in blood volume, and decrease in BP. A decrease in ADH secretion results in an increase in H2O output. A increase in ADH secretion results in a decrease in H2O output.

Na+ absorption also affects urine output. If reabsoprtion of Na+ is inhibited (by caffeine for example), it causes an increase in H2O output.