Hold the flute out in front of you and locate the pin you would like to remove. Attempt to straighten the pin if it is bent by using the tips of the needle-nose pliers and clamping down on the pin.
Apply a few drops of synthetic oil to the part of the pin that connects with the braces. Don't worry about using too much oil, but avoid getting the key pads wet.
Place the tip of the needle-nose pliers on the left side of the pin, near the brace that holds the pin in place on the left. In a side-to-side motion, attempt to wiggle the pin out of the brace and free it from the flute.
Apply a small amount of heat to the pin using a match if oiling doesn't work and you don't mind ruining the pin. The heat will help to loosen the pin from the flute. Alternatively, you can use hot water to avoid damaging the pin, but be very careful to avoid getting the flute key pads wet.