This is probably the most difficult part of the entire building process. I have seen numerous different approaches to controlling the ROV. Jason Rollette used a microcontroller, which is really the best way to go. He has full analog control of all motors, and at the data is transmitted up a Cat 5e Ethernet cable. However, unless you have the means to print out a circuit board and program a microcontroller, this is not the easiest to assemble. Jason has a diagram of the circuit and the PCB on his site here
Alternatively you could use relays to switch the motors on and off. this is not as good as full range control, but it is much simpler and straightforward. At Homebuilt ROVs
, Steve used relays to control the Seafox, and he has a good guide to assembling any number of relay controlled motors.
This is one of the 4 speed controllers I am using for the thruster control