Tidal Mechanics

As both the Earth and the Moon move, so does the water. The overall result of what is quite a complicated dance is that there are two tides a day, although they actually take a little longer than a day. One high tide is experienced when a point on the Earth is facing towards the Moon and the other is when that same point is facing away from the Moon as the Earth rotates. The Sun also plays a part. There is also a lag effect as while the Earth is spinning, the Moon is orbiting around the Earth and so has moved on a little in the sky while a day relative to the Sun has taken place. There are myriad other effects, such as seasonal, atmospheric and oceanic current action, that combine and compound to result in the actual tides.

The mutual gravital attraction between the Earth and the Moon is such that all Earthly matter shares a longing to join with the Moon and so what is not tied down can move that little bit more easily in the direction of the Moon. For water connected as a continuous body on a spinning planet, that region of water nearest the Moon effectively raises in level and is bulged towards the Moon, thinning around the Earth at parts farthest away facing the Moon, with resultant currents and relatively inertial forces also joining in to cause a shallower, complementary bulge at the farthest distance on the far side of the Earth. 

Note the word "effectively" in that explanation. Just as the water wants to go to the Moon, it also wants to keep going towards the Earth, the water does not leap directly into space, it stays on Earth. At each point on the oceanic globe, there is a force towards the Moon, there is force towards the Earth, there is the overall force of the whole Earth towards the moon. At points on the globe that are that farthest away yet still on that surface facing the Moon,  the observation is that the tidal weight of water is lowered as the Earth rotates.

The gravital effects on water can be paraphrased as four forces;-

1) The force between Earth and its oceanic waters

2) The force between Earth and the Moon

3) The force between water and the Moon

4) The force between water and water.

There is also the hydromechanical effect of currents and there are forces such as precipitation , evaporation, storms, planetary vibration, earthquakes, geothermal vents, salinity gradients, gaseous effluxes and obstructions to flow that affect these currents.

Typical Explanation

A vector force description may help understanding by disassembling simpler explanations as to how and what is happening. There may be;-

1) A force from a point in the ocean, i.e. effectively on the surface, to the centre of the Earth. This point represents a volume or mass of water.

2) A force shared, subsumed, with the rest of the Earth aiming straight towards the centre of the Moon from a notional centre of the Earth. 

3) The direct attraction aimed straight at the Moon from the point in the ocean. 

These points and centres are theoretical constructs to help describe the forces acting. There is no actual force pointing to the centre of any planet. There is an overall summation proposed that as a single number is associated with a direction as if towards the centre of whatever is being looked at. The force is also a mutual force, it takes two items minimum for an attraction, so that the attraction has two directions.

1) is a contributory force, 2) is a contributory force and 3) is termed the resultant force, or what happens when you add 1) and 2), but here is better thought of as being the original force. 

The first force is locally aimed straight towards the centre of the Earth, not at the Moon. It indicates that the water experiences an Earth centripetal force that also interacts with the Moon force.

One vector explanation is that if you take the direct force, 3, and have to physically express it by reference to the centre of the Earth, it translates as the two contributory forces, 1 and 2.

You could also view that the Moon, casting forces, waves and vectors in all directions, diminishes that component of Earth's gravity less at the farther away places within the Moon's Earth horizon and moreso nearer the Earth.  You could view that there is the movement of the solid Earth within its encapsulating bubble or envelope of water towards the Moon such that it pulls away on the Earth's far side from the envelope creating the far away bulge and causing a thinning at right angles to the direction of movement with a corresponding gorging of water on the side nearer the Moon.

Comment

So far a clear explanation of tides is not a closed book item, even in basic terms so that the challenge is still out there to come up with one.