I have a gigabyte motherboard,It has a small fan in the middle of the board,but it never runs.Is this fan supposed to run or what??

What is the model of motherboard? (for example - GA-K8NF)

If a fan was fitted to the board when you got it then it should run. Check to see if the connector is properly connected to pins on the board.

Make sure you ground yourself to get rid of static electricity before touching the insides of oyur computer