These are called Differential Forces and they act on Earth to distort it. The `solid' Earth is rather ridged, and distorts only a bit (making the Earth somewhat `oblate'. The Oceans are more easily deformed, and this leads to the Ocean tides seen.

A Simple Tidal Model
Imagine a planet entirely covered with Ocean. The liquid at point A (on the left) is closer to the Moon and experiences a larger gravitational force than point B or the ocean at point C. It is pulled away from the Earth, toward the Moon, thus producing the bulge on the right side. The left side bulge arises because the Earth is pulled away because the moon's gravitational force at point B is larger than at point C. As our ocean planet rotates under these bulges, a given point on the surface will experience two high and two low tides for each rotation of the planet.

Tides in Real Life.
The tides seen at a given location is a bit more complex than this, depending on latitude, shape of shore, depth of ocean and inlets, winds, etc. Typical tides are a meter or two. The Bay of Fundy, in Nova Scotia Canada, experiences tides up to 40 feet! Another areas with large tides include, the Gulf of California (Sea of Cortez) with 24-foot tides at the top of the bay. The Gulf of Mexico experiences just one, 1-foot, tide per day!