To delete all of the songs from an artist, tap the “Edit” button, tap the red “-” next to the artist’s name, and then tap the “Delete” button that appears. If you want to delete an album or an individual song, turn Edit mode off so you can navigate through your music. Tap an artist to see all of the albums from that artist you have on your device, and then tap an album to see all of the songs. When you’ve found something you want to delete, tap the “Edit” button, tap the red “-”, and then tap the “Delete” button.
If you don’t want to use iTunes, you can use a program like Sharepod, but nearly all third-party programs still require iTunes to be installed in order to work. Still, they can be very useful if you’re trying to manage your music on a computer that isn’t yours and you don’t want all of your music deleted when you sync. Click here for more instructions on using a third-party program.