Under the new Codes...all dryers (and stoves/ovens) must now be 4 wire....having a seperate neutral and ground wire in NEW construction. In decades past, the neutral was allowed to serve as both - the neutral and ground - typically by means of a solid metal strap or wire strap that bonded that connection to the metal frame of the dryer. This sounds as if it is the case in your existing dryer...which was typical.

But...the old arrangement wasn't always reliable...and a seperate dedicated ground provides a greater safety path in the event of a fault inside the dryer (lowering the chance the user may get a shock when touching the frame of the dryer).

To modify your existing 3 prong dryer over to 4....you'll need to remove the 3 wire - disconnect the ground strap (or wire) that bonds the neutral to the frame of the dryer...and install your 4 wire so that you'll have (from left to right) one hot, one neutral, one hot connection...and connect the ground directly to he frame of the dryer (there is usually a green screw near the dryer connection block for this ground)

For more on this - with an illustration, see:

http://www.american-appliance.com/service_pages/electric_dryer_cord.htm

When done properly, you can test for correct wiring and connection with an ohm-meter (continuity check)...by checking for continuity from the ground prong on the plug to the frame of the dryer...you should see continuity. Then check for continuity from the neutral prong on the plug to the frame...you should NOT see continuity....nor should you see any continuity between the neutral connection at the wiring block to the metal frame.

The whole purpose of the Code change to the 4 wire is to seperate the two.

Hope this helps,....if you need more details, please follow-up.