Calculating transfer function


If I had two waveforms as audio signals, how do I calculate their transfer function? If getting an actual mathematical function is hard, a list of 100 or so values of the function would be fine too.
Mhhh ... Do you mean Z-transfer function maybe? If F(z) is the Z-transform of the input sequence, and G(z) the Z-transform of the output, S(z) = G(z)/F(z) should be an estimate of the transfer function of your system.
Do you mean the transfer function mapping one to the other? That's not necessarily uniquely defined. Normally a transfer function is inferred from an impulse response or from some other signal with all frequencies present such as pseudo-random noise or a chirp signal.

You can take the Fourier transform of both waveforms and divide one by the other (which is why you don't want every frequency present to avoid dividing by zero).
I am quite new to audio so I am confused. Let me provide some more context. I am basically trying to generate a list for Waveshaper from an audio file of a predefined sine wave running through different guitar pedals. I'm not too sure how the 'mapping' of -1.0 to 1.0 works either, but I know I have to provide values of a transfer function between the sine wave and the audio file. Could you give me some explanation?