In my shower I have a three handle system. When I turn on both hot and cold the turn the shower handle to divert the water to the head, the hot water comes out of the shower head but the cold water comes out of the water spout. How do I get the cold to go to the shower head?

How old would you say the system is?

The middle handle in the old styles had washers and seats which would wear out,replacement required a special tool(seat removal tool) and most likely the replacement of the brass screw holding the washer in, sometimes even the cup which surrounded the washer..

I don't know about new ones,perhaps there is a way to find out what the innards are like without removal,look for the brand name,check online for the maker and try to find the exact system, a diagram might show you the problem, and there might even be a trouble shooting section.

Otherwise,it's call the plumber time(IMO)