There are thousands of solutions with almost all of them working. I can only guess the astounding number of solutions is what stopped you cold.
I will note the AUDACITY is what I use for the recording software as it is free and I can clip the recording up to drop the stuff at the beginning and end where I needed it.
Radio Shack has cables, adapters so you can run your RCA jacks to the Line In so that's too easy.
I have an extensive library of stereo tapes which I would like to covert to digital format. Is there an adapter that will take the RCA lines used by the tape deck and connect them to the computer via USB connector? I assume I would need some sort of software as well for the computer?