Ocean tides are caused by the complex interplay of three astronomical bodies: the Sun, the Earth and the Moon. Both the Sun and the Moon exert a gravitational pull on the Earth's water. The resulting force of the Moon's gravity creates two tidal bulges on opposite sides of the Earth. Depending on the relative position of the Sun, the tidal bulges will change slightly as the Moon experiences its phases.
Full Moon and New Moon
At both full moon and new moon, tides are at their most drastic. High tides are very high, and low tides are very low. At full moon, the Moon and Sun are in a straight line on opposite sides of the Earth. Their gravitational forces combine to create larger tidal bulges. At new moon, the Moon and Sun are in a straight line on the same side of the Earth. In this case, their gravitational forces still combine to create large tidal bulges. These situations are called spring tides.
At quarter moons, the Earth's tides are at their least drastic. When the Moon is at a quarter phase, it forms a right angle with the Sun (with the Earth at the vertex). The gravitational forces from each body act at perpendicular angles, diminishing the overall tidal bulge. The Moon is still exerting a stronger gravitational force than the Sun, so there is still a net tidal bulge. However, this bulge is at its smallest. These situations are called neap tides.
Waxing Gibbous and Waning Crescent
During the waxing gibbous and waning crescent phases, the Moon is approaching its full and new phases, respectively. Because of this, the resulting tidal bulges will increase in size until they reach their maximum during the spring tides.
Waning Gibbous and Waxing Crescent
During the waning gibbous and waxing crescent phases, the Moon is on its way to the quarter phases. Because of this, the tidal bulge will decrease until it reaches its minimum at the neap tides.