I purchased the "controller companion" to try to hook-up my Microsoft Xbox 360 wireless controller to the World of Warships. Is there any concise documentation on how to do this.

I don't know about "Controller Companion", but if you want similar functionality in other programs, you could also try FreePIE. Here's a starter script to get you going, in case you use it:

index = 0  # Joystick index
dz = 100  # Deadzone


### CONTROLLER BINDINGS


snes_left = joystick[index].x < -dz
snes_right = joystick[index].x > dz
snes_up = joystick[index].y < -dz
snes_down = joystick[index].y > dz


snes_a = joystick[index].getDown(1)
snes_b = joystick[index].getDown(2)
snes_x = joystick[index].getDown(0)
snes_y = joystick[index].getDown(3)
snes_l = joystick[index].getDown(4)
snes_r = joystick[index].getDown(5)
snes_start = joystick[index].getDown(9)
snes_select = joystick[index].getDown(8)

### KEYBORD BINDINGS

keyboard.setKey(Key.LeftArrow, snes_left)
keyboard.setKey(Key.RightArrow, snes_right)
keyboard.setKey(Key.UpArrow, snes_up)
keyboard.setKey(Key.DownArrow, snes_down)


keyboard.setKey(Key.X, snes_a)
keyboard.setKey(Key.Z, snes_y)
keyboard.setKey(Key.LeftShift, snes_b)
keyboard.setKey(Key.Escape, snes_select)
keyboard.setKey(Key.Return, snes_start)

Another option would be XPadder (pretty easy to use, and there's a free version around), or Pinnacle Game Profiler (though that requires that you buy it).