Question

how will you prove that air contains water vapour in it

Answer 1

Just take a cold glass of water and place it anywhere for a while. You will see drop of water outside the glass. As the water vapors in the air strike the cold glass, they loose their kinetic energy and condense on the outer surface. That's why you see the water outside glass.

Answer 2

we can show it by the following activity.
fill a glass with cold water. you will observe some water droplets . this shows that air has water vapour in it which loses its energy and get converted into water .