Help Designing A motor Control Circuit

You have a circuit that shorts the power supply out when either relays is activated. Have a careful look so you see why...

Look at the last two circuits on Grumpy Mike's motors page:
http://www.thebox.myzen.co.uk/Workshop/Motors_1.html

These use relays with changeover contacts (most relays are of this type), either SPDT or DPDT.

The relay coils must have flyback diodes across them (or you will destroy the circuit with the high-voltage inductive pulse at switch-off).
If the relay(s) take more than 25mA or so you will need a transistor to amplify the current from the Arduino pin - Arduino outputs cannot tolerate 40mA or more, you again risk destroying the device. There are many examples of how to drive relays around. You will need to find a relay that can handle the output current (with a good safety margin), then choose a way to drive its coil.