The papers you found seem to me quite good references, I've read them briefly and will surely want to study them thoroughly, +1 for that. But your question does not seem to make a lot of sense, or at least it does not have a viable answer.
The procedure is an extremely complex one (as you've realized by the reading the papers) and is built on multiple layers of basic calculus, Fourier tranforms, audio engineering, signal processing, etc. You can't understand the procedure without understanding the theory.
Also it's not humanly possible, in practical terms, to manually encode an audio file by hand. You have to do literally thousands (probably hundreds of thousands, for a complete MP3 implementation) of complex arithmetic operations just to encode a single audio frame of, say, 512 samples. That's just about 0.01 seconds of music at 44.1KHz sampling rate.
Perhaps you should aim your learning efforts at less advanced stuff to begin with?