Question

how does air exert pressure

Answer 1

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HERE IS YOUR ANSWER,

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==> Our atmosphere is a layer of air covering the earth from all side. Atmospheric pressure is caused by the weight of air molecules above the atmosphere. The layer of air exerts a force on the surface of the earth. The force per unit area, by the atmosphere, on the surface of any object on the earth is called atmospheric pressure.
At the sea level this pressure is equal to 101325 Nm-2. As elevation increases, fewer air molecules are present. Therefore, atmospheric pressure always decreases with increasing height.

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Answer 2

hope it will help you