On the ex-headphones cable you've likely got two coax connectors (formed together in a figure of 8 - split them first) - one core will have a braid (outer wire shield) and a likely a red wire 'inside it' - ther other the same with a white wire inside it. Twist the braid together on each wire to form a 2nd 'wire'. (so 4 wires total)
What you basically need to do is connect the internal red wire to the red phono(RCA) central pin and the outer braid/shield to the outer part of the phono(RCA) plug. Do the same for the white.
Just hold them on there to test, when you get sound then you can go about making it a bit more permanent. Doing a direct wire to wire connection (2 left, 2 right) is the only option if you're not going to use the proper connectors as trying to attach wire to a phono plug is a no-no ...
I hope this helps ...