What is the best way to control 4 motors?

I have the relay shield produced by Seeed Studio and I would like to know what would be the best way to control these motors. I have a thumbstick from a ps3 controller that was broken or I have momentary switches. 2 motors need to control up-down and the other 2 need to control turning and going forward.

How many of the motors need to be able to go both directions?

Maybe some push buttons so you can digitally talk to the Arduino. The Arduino can read the digital HIGH's and LOW's from the buttons and control the motor shield.

You can use the below switch to control the direction of operation of a motor.