Without the moon, the earth would probably still have some tidal action because of its rotation on its axis and the way the tilt of the earth causes it to face the sun differently in the changing seasons. No one would ever build a surfboard to ride those waves unless a storm surge assisted their rise. This would no doubt have a dramatic effect on the life at the areas continually covered and uncovered by water. Some of the nutrients that are stirred by tidal action would also not be available to any life above the ocean floor.
The moon being about a quarter of the earth's size is a fairly strong gravitational influence at only 238,000 or so miles away. The gravity of the moon pulls on the entire earth. It may even influence some of the movement of the terrestrial plates. Its power over the liquid water on the earth is the most profound and easiest to prove and observe. It exerts a two-fold influence as the earth rotates on its axis, and the moon also orbits about the earth.
As the earth spins on its axis, the gravity of the moon pulls and tugs at different points on the earth. Using North America as an example, as the moon passes onto the eastern seaboard, it pulls the water in the Atlantic Ocean toward the continent. This creates a rising tide. When it reaches the mid-point of the continent, its pull on the Atlantic begins to wane while the moon's gravitational effect on the Pacific Ocean is increasing tide levels on the west coast. As the rotation continues until the moon is at the center of the Pacific, the waters from both sides of the Pacific are pulled away from the continents creating two low tides simultaneously. This process goes on day and night continually.
In addition to the straight pull of the moon on the earth's oceans, it also has an effect on the orbit of the earth itself. The moon orbit's the earth every 28 days. Because this isn't a rapid rate, the effect is to create a gentle wobble for the earth. This wobble also affects the ocean waters to a lesser degree just as a slow steady movement on a bowl of water causes the water to move back and forth.
Finally, sometimes the moon and the sun conspire together during the moon cycles to create additional tidal influences. This occurs because in order for the moon to cycle, the sun and moon move into differing planes in regard to the earth. Depending on where in the earth's rotation and the moon's orbit this occurs, extra high or extra low tides can happen. At other times, this may serve to moderate the tides.