How to denoise a conversation between two people?
I think what you're attempting to do is a case of blind source separation (check Wikipedia). There are many techniques to solve this kind of problem, maybe you could check those on the Wikipedia and use the one that fits your needs best.

Particularly, last year one of my teachers showed us a demo of the ICA algorithm, and we got to play round with it in MATLAB. It seemed really effective, and there's a research group that even created this MATLAB toolbox for the ICA algorithm. Here you can check a simple demo (called cocktail party problem) of how ICA works and how effective it is.

Since you say you're new to DSP, I'm not sure if ICA or the other techniques would be too advanced for you, but maybe this will put you in the right direction. Good luck.