Carefully insert an iPod opening tool in the seam between the metal casing and white plastic top. Be careful not to damage the soft plastic with your tool.
The new Nano more closely resembles the old Mini design than the previous iPod Nano generation.
Pry out the headphone jack slowly with a spudger. Do not remove the headphone jack entirely, as it is connected via a fragile ribbon connector to the click wheel.
Disconnect the headphone and click wheel cable from the logic board. It's tricky to see what you're doing, so you'll have to feel the connector inside the iPod with the spudger.
You need to pry the connector toward the front of the iPod until it comes loose from the logic board.
Do not entirely remove the headphone jack. The cable is still connected to the click wheel.