Unlike halogen lamps with a simple two-prong base that pull straight out of their sockets, gu10 lamps have a cylinder at the base of each prong are wider than the prongs that connect the lamp to its socket.
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Stand on a ladder so you can comfortably reach your light fixture.
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Press the existing Gu10 lamp into the fixture using both thumbs.
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Turn the lamp counter-clockwise as you continue to press inward, using the pressure of your thumbs to grip the bulb.
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Release your pressure on the lamp when it won't turn any farther.
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Pull the lamp straight out of the socket. You may need to wiggle it gently to get the cylindrical "feet" aligned correctly with the larger openings in the socket.
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Discard the old lamp and remove packaging from your new lamp. Line the prongs on the new lamp up with the wide openings on the socket.
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Press inward on the edges of the new lamp with your thumbs and twist the lamp clockwise as far as it will go.