You must have at least one LCS save file on your Memory Stick to start off with, and you can't just play music you've already saved on your Memory Stick in the game.
Song names and other info will be shown so it's easy to find your favourite tracks.
Then you use the PSP's left and right button to switch between songs, instead of changing radio stations. Once you've downloaded the program (you can find it on the official LCS website) you can rip tracks from CDs, convert them to the right format and stick them in the game. Rockstar has released a new Custom Tracks feature for GTA: Liberty City Stories, the first PSP instalment in the Grand Theft Auto series.