Remove background noise from recording
The signal seems non-stationary, at least less stationary than the noise, and the noise is of relatively lower amplitude. Hence, a class of methods resides in performing one or several non-stationary transformations (time-frequency, time-scale, or  spectrograms and wavelets). They can concentrate useful signals on a little amount of coefficients. Then, thresholding or shrinkage techniques, reducing low-coefficients and preserving higher ones can be interesting.

Free softwares like audacity have build-in functions. For more techniques, you can check for instance:


VOICEBOX: Speech Processing Toolbox for MATLAB, esp. Spectral noise subtraction.


More advanced techniques, termed "source separation", are for instance described by:


FASST: Flexible Audio Source Separation Toolbox