If you were able to kluge together a frankenstien system, you must have some basic understanding of how to connect the pieces together. What are your specific questions?
The Adcom kit is pretty dope, so let's work with that to start.
Where does it start? Well, from a music content standpoint, it starts with the source components (the tuner, disc player, and tape deck, or anything else that has analog output, including whatever it is you're using in your franken rig). Connect those components to the corresponding inputs on your Adcom preamp using rca cables. Do not connect any of those components to the "phono" inputs, as that input is for a turntable's output. The phono pre in the old Adcom is quite good, if you ever decide to add a tt.
Next, connect the preamp to the amplifiers (yes, you have two amps, the Adcom and the onboard amp of the sub). That Adcom preamp has three sets of pre-outs to choose from. The "bypass" preouts bypass the internal tone controls, but neither the "lab" or "normal" outputs do, so if you plan to use the bass and treble controls on the preamp, be sure to use the "normal" or "lab" pre-outs. After you have decided that, connect one set of pre-outs to the Adcom amp's inputs, and another set to line level input on the sub.
Finally, connect the amp to the speakers using speaker wire, observing phase.
That's really about it. You have some controls on the back of the sub which you'll use for calibration (blending the sub with your main speakers).