If you bought the "super clean" servo leads, you connect the one with three wires to channel 1 on the receiver and the top-left three-pin connection on the controller. Be careful to get the (black) ground lead to the outside on the KK2, and bottom on the Turnigy receiver. Then you connect the next three single leads in the ribbon to channels 2, 3, 4, & 5, in order to the INSIDE pin on the KK2 and top pin on the receiver.
If you just bought regular servo leads, connect channels 1-5 to the left connections on the KK2, again with the black lead to the outside on the KK2 and bottom on the Turnigy receiver.
At some point, you will want to map or bind a control knob or switch to the fifth channel, but that can wait. The reasons for having that "aux" control will be made clear during the KK2 configuration process.
There are a lot of videos on Turnigy binding; I've linked to one of them. If you find it unhelpful, search for another. Basically you have to get the radio and receiver in such a mode that they go looking for partners and establish an identity link with one another. You should only have to do this once. With the Turnigy, this is done at the receiver end with a little wire jumper that is supplied with the receiver. I went through the steps above because you can power the receiver THROUGH the KK2 (and that through one ESC, ultimately taking power off your flight battery). The video instructs you to use an auxiliary power source from four batteries. You are free to do either one, but the receiver must have 3.3 - 5v (6v works) in order to bind. If you don't use an auxiliary power source, rigged to the receiver, you will need to have your flight battery charged, and the wires connected to your ESCs.
Once your receiver is connected and bound, and your radio is on, you can proceed through the KK2 configuration screens which resolve any swaps or issues with channels.
When you connect the four ESCs to the KK2, I'd recommend you only power the KK2 from ONE of them. Meaning you cut or remove with a very small needle the center wire from the three-pin connector of THREE of the ESC/control cables. That is generally the RED wire. You will see there are three tiny flaps on one side of that connector, and lifting one with a needle while pulling the wire back with tweezers is best. Then wrap the bare connection with a bit of electrical tape. Again, those wires are pretty standardized with the black always being ground (which you need for control signal), the red being power, and either yellow or white (Futaba) for control signal. As with the receiver connections, you will find that the ground lead is closest to the edge of the KK2 board.
There are good YouTube videos on KK2 setup. If you cannot find one, I'll be glad to help.