The Moon's Gravitational pull varies across the Earth
The orange arrows in the above diagram show the strength of the gravitational force of the Moon on different parts of the Earth. You can see from the length of the arrows that the force on the side nearest the Moon is stronger than the force acting on the centre of the Earth. This in turn is stronger than the force on the opposite side to the Moon.
Show > Stage 2
Tidal force also varies across the Earth
However, tides are caused by the difference in the forces between the surface of the Earth and the centre. The blue arrows now show the effect of the difference between these forces. This is the tidal force. Thus the overall force is toward the Moon on the lunar side of the Earth and away from the Moon on the opposite side.
Show > Stage 3
Water flows to peaks of the tidal force
Because the rock of the Earth is solid, it is not changed by the tidal force, but the water is able to move more easily and flows to form a bulge in both directions - toward and away from the Moon. As a result we get two tides, one when the Moon is above us, and one when it is on the opposite side of the Earth.