The Sony PSP was not actually designed for the purpose of playing music. It was created to be a mobile 3D-game machine, a bit like the GameBoy was for the 2D world.
However, very often it occurs that those little technical gadgets get used for other things than what they were origianally designed for.
Actually the PSP game console is able to play both music and movies and the sound quality is very good.
While it is not common that songs are being sold on UMD (the PSP media format) you can easily take MP3-songs that you already have on your hard drive and copy them to the PSP.
If you want to transfer audio CD tracks to your PSP, you have to first convert the music from the CD on your computer and then on to the PSP from the computer.
Here is what you need: a PSP-memory card large enough to store the music files, a USB cable to connect the PSP to your computer and a CD ripping software in case you want to convetr your existing audio CD collection to the PSP.
You can also get software that takes care of all of that. It can extract the music from the CDs, convert them into the right format for the PSP and then transfer them on to the PSP.
Some pieces of software like this can also compile a music library on your computer and remember which songs you have on your PSP so you won't accidentally put them on twice and waste memory.
If you have one of these programs, you just need to connect your PSP to your computer, start the program and press the "synchronize" button.
The best thing about downloading music on to your PSP is that it doesn't have a proprietary format, like the iPod with iTunes. While the PSP was not designed as a music player, it is definitely handy to be able to enjoy your MP3 collection on your game console.