Playing back music is a pretty essential and simple task: Just tap the Space bar. Troubleshooting playback is pretty simple, too:
Remember that you’re now contending with two different volume levels: your Mac’s own speaker volume (which you can adjust with the volume keys on your keyboard, or using the Sound panel of System Preferences) and the little volume slider at the top of the iTunes window. Adjust both of them.
If you can’t hear anything at all, make sure that you don’t have external speakers or headphones plugged into your Mac (which cuts off all sound to the built-in speaker).
And if you have an AirPort Express wireless networking base station, make sure that the pop-up menu at the bottom edge of the iTunes window is set correctly. If you’re trying to play back the music using your Mac’s built-in speakers, make sure this pop-up menu says Computer. And if you’re attempting to direct playback to whatever speakers are attached to the AirPort Express, make sure they’re turned on and hooked up right.
It’s a feature, not a bug. Choose iTunes → Preferences, click Audio, and turn off Crossfade Playback.