Now use the 20-pin socket and female headers to make a cradle which connects the pins from the cable to the right pins on the chip.
The first thing to do is superglue all the headers and the socket to the circuit board. That way, it's easier to solder to. You can even make an extension for the header like I did if you need more room on your circuit board.
The wiring is as follows:
Cable ATtiny2313 PinMOSI 17MISO 18SCK 19RESET 1GND 10
Get yourself the short ATtiny2313 overview
to double-check the pinouts.
And remember: you're soldering up the wires on the underneath, and it's mirror-image. It might help to mark where pin 1 is on the bottom side before soldering. (I did it wrong once. Once.)
That said, the wiring is very simple. Just pin to pin, and then connect all the header pins to the closest pins on the socket. Fortunately for me, this pre-printed circuit board from Radio Shack did the trick.
The cradle is versatile too. See the last picture for my ATtiny13 programmer cradle. I have another for an ATMega8 too.