The following diagram shows how the moon causes tides on Earth:
In this diagram, you can see that the moon's gravitational force pulls on water in the oceans so that there are "bulges" in the ocean on both sides of the planet. The moon pulls water toward it, and this causes the bulge toward the moon. The bulge on the side of the Earth opposite the moon is caused by the moon "pulling the Earth away" from the water on that side.
If you are on the coast and the moon is directly overhead, you should experience a high tide. If the moon is directly overhead on the opposite side of the planet, you should also experience a high tide.
During the day, the Earth rotates 180 degrees in 12 hours. The moon, meanwhile, rotates 6 degrees around the earth in 12 hours. The twin bulges and the moon's rotation mean that any given coastal city experiences a high tide every 12 hours and 25 minutes or so.