Use a USB cable to connect the iPod to a computer that has iTunes installed on it. The iTunes application starts automatically when the computer detects a connected iPod.
Click on the iPod icon in the upper left corner of iTunes. Click Music under the "On My Device" heading near the bottom of the menu on the left of the screen.
Uncheck the boxes next to the songs you want to remove. These songs are then removed from the device and from future syncs.