Find your VC Stories save folder on your mem stick. Usually, it is named ULUS10160S92F0.
Now, you're going to create a new folder, and name it ULUS10160CUSTOMTRACKS.
There are two ways to get your music into the proper format(.gta) so you can listen to it in VC Stories.
Download R* Custom Tracks(if you don't have it already) at http://www.rockstargames.com/libertycitystories/gta_lcs.html
Install it, and insert the CD with the music you want in VC Stories.
Convert your tracks, save them to the desktop. Insert these new files (.gta files) into the ULUS10160CUSTOMTRACKS folder.
PC Music Files-
Download Exact Audio Copy PSP Edition from http://www.megaupload.com/?d=46HIYRIQ
(you have to register first).Install the app, and drag your music files onto the client.
It will convert them to .toc format. Now, make sure Window's allows you to see file extensions. If it doesn't, go to Tools>Folder Options>View Tab> and uncheck the box next to "Hide extensions for known file types". Now, click the .toc file that EAC created for you, and change the extension from .toc to .gta. Insert all your converted files into the ULUS10160CUSTOMTRACKS folder.
Either way you choose to do it, your ULUS10160CUSTOMTRACKS folder should look something like this:
Note: Your file icons will vary, most of them will be the default "Windows Unknown File Format" icon.
Now, run VC Stories. When you load your game, pause. Go to audio options, and change the Custom Tracks option from OFF to ON.