Question

how do the gravitational force between earth and moon causes waves in the ocean?

Answer 1

Winds and currents move the surface water causing waves. The gravitational attraction of the moon causes the oceans to bulge out in the direction of the moon. Another bulge occurs on the opposite side, since the Earth is also being pulled toward the moon (and away from the water on the far side).

Answer 2

There is a very straightforward logic behind this actually.

Earth and moon always attract each other with equal forces, but moon causes very little acceleration ion earth due to earth's large mass, so it tries to pull off every possible thing on earth and since water is a fluid- it pulls on it. It is actually the combined force of gravity of sun, moon and earth that causes tides. When the sun and moon are aligned (that gives us the new moon, i think) the force exerted on the oceans is more and it causes very high and very low tides, these tides are usually called spring tides.
when sun and moon are opposite, their gravitational forces cancel out and such dramatic tides do not occur.

Correct me if I am wrong. :)