Question
How close do I need to plant Italian cypress trees to create a tight hedge that people can not see through?

Answer
They are about 5-6 feet wide at maturity so if you plant them 3 feet apart they will grow into a complete solid hedge. These are pretty tall also about 40 feet if left to grow. They can be pruned to the height you want them.
When you plant them make sure the hole is twice the size of the root ball and as deep. Fill the excess with good top potting soil and mulch around the trees with not more than 3 inches deep of organic mulch and water.