To assemble the ESC to your motors, you have to link the part with 3 cables, with the 3 cable from the motor
To assemble the ESC to the power, you have to link the red one to the positive side of the battery, and the black to the negative side. It will help to have a distribution power board, to keep it organized, since you have to link 4 ESC to the battery
To assemble the ESC to the control board, you have to connect the 3 colored cables(the thin ones) to the right side of the board, with the black or brown cable to the edge of the board. You don't have to connect power to the control board, these colored cables already bring the power.