Here we explain how to get started in using the iPhone music player to play music. There are other music apps available such as Ecoute and Groove. Other players have other functions such as integration with Last.fm in the case of Groove and they also have social functions integrated. For basic music playing the built in player works just fine.
Choose a playlist, song, or artist and tap it.
Apple has a great list of music apps that you can check out. Nobody does music better than Apple. You can also read about how to copy music from your phone to a PC or adding music from saved files and CD's to your iTunes too.