Track 1: You new sub must have two pair of connectors like the "Low Level" ones shown in the upper right of this:
So you'd run two RCA cables from the stereo out (red & white) of your source component to the corresponding "In" of the sub. Then, run two cable from the "Out" of the sub (again red & white) to the corresponding Input of your Sony system.
Track 2: If your new sub does not have "Out" jacks (as shown below) then you'll have to have a source component that decodes the signal into its various parts (left front, right front, center, etc.). One of these parts is for the low frequencies. (That's the .1 of a 5.1 system.) You'd run a cable from the "Sub Out" of the source to either of the "Audio Jacks" (doesn't matter which) of the sub. The other 5 cables go to the back of the Sony. (You may want to get a "Y" splitter and split the "Sub out" and run it to both the new sub and the Sony.)
Hope this helps.