The original indicator actually has 2 "Hot" wires. When you put the left signal on, the 12V goes to the indicator on one side of the the bulb and "grounds through the right side blinkers (right through the bulbs). The 2 signal bulbs are low enough resistance to ground, that they act as a straight wire to ground. The reverse happens on a right turn. With LED signals, that low "ground" current is still enough to light the LED signals, so the diodes are used to prevent it. So now when the left signal is on, you go through one diode, the other prevent feeding back to the right side, and the power has to go through the indicator bulb (or LED) and then directly to ground.
Hope that helps a little.
The 2 red wires are easy, one to the original indicator wire (or "left " signal hot wire, and one to the other indicator (or "right" signal hot wire).