You rectify the music to give a varying DC voltage according to how loud it is (just like any VU meter), then simply read that DC voltage with the ADC in the PIC, and display it as you wish.
A LONG time ago I did just such a project, using a 16F876 feeding two multiplexed rows of 16 LED's for a stereo VU meter. I also used another two input pins to switch the display between linear and logarithmic, and dot and bar - you need the logarithmic display for a VU meter. Essentially it was an enhanced stereo version of the LM2914/5 LED meter chips.
In fact, asking about generating the logarithmic display was the first question I ever posted on here - unfortunately I've long since lost all the details and code, but I wrote a Delphi program to generate a logarithmic look-up table that the PIC used.