Songs can be removed from an iPod through the use of iTunes. Connect the iPod to the computer and open iTunes. Click on the music tab and then click on sync music. From that screen check on the songs that you want to sync to the iPod, any song that is not checked will be removed from the device.
First you will need to connect your iPod to the computer and open up iTunes. Next you will select your device and then select the song that you want to delete. You will then right click and select remove. This will then delete the song from your iPod but not your iTunes library.