Use a craft knife to pry the white plastic piece off the top of the iPod. The on and off switch is located on the white piece. Stick the knife down the side of the piece and lift up to remove it.
Repeat Step 1 to remove the second white piece off the bottom of the iPod where the headphone jack is located.
Look for two tiny screws on both the top and bottom of the iPod shuffle where the on-off switch is and where the headphone jack is. You will see one screw on each side of a metal plate. The screws are holding the metal plate down. Use a tiny screwdriver to remove the two screws on each side, totaling four screws altogether.
Use the tip of the screwdriver to remove the metal plate on the top and metal plate on the bottom. Stick the tip of the screwdriver underneath the plate and lift up on the plate. Both will easily pop out.
Put your screwdriver on the small flat metal piece on the bottom of the iPod and push the board out. You will see a flat area next to the headphone jack with a negative sign on it. It is better to push the inside out from this surface, so you do not damage the board. The board will slide out from the outer case easily.