The easiest method is to connect your iPod and launch iTunes. Then select the songs you want to erase and remove them. There are detailed guides for this available online.
You'll need a cable to connect the iPod to a computer (depends on the model). Once it's connected, use the iTunes program to edit the music that's stored on it.
You must download iTunes. Connect the iPod to the computer using the USB port and open iTunes. Click on the iPod when it appears then restore. This will delete everything.