How does the moon affect the tides?

Gravity is one major force that creates tides: in 1687 Newton explained that ocean tides result from the gravitational attraction of the Sun and the Moon on the oceans of the Earth. The pull is not uniform. Ocean waters on the closer side of the Earth experience a greater gravitational pull from the Moon than waters on the opposite side, which raises a bulge in the water nearest the Moon and a high tide there; at the same time, inertial forces on the far side raise a similar bulge and a second high tide. The result is a standing distortion of the ocean that the planet rotates beneath, so most coasts pass through two high and two low waters as it turns.

Tidal generating forces vary inversely as the cube of the distance from the tide-generating object. That cube is why the small, near Moon beats the vast, distant Sun: the Sun's tide-generating force is about half that of the Moon, and the Moon is the dominant force affecting the Earth's tides. Mass alone would favor the Sun overwhelmingly; proximity overturns the comparison.

When the Sun and Moon are aligned, at full or new moon, their gravitational forces act in the same direction and produce more pronounced high and low tides, called spring tides. When they stand at right angles relative to the Earth, the Sun's pull partially cancels the Moon's and the result is the less pronounced highs and lows called neap tides. Local geography then does the rest: the same astronomical forcing produces a barely noticeable rise in one basin and a dramatic one in another, depending on the shape and depth of the coast.