Short answers, pulled from the story.
The Moon pulls on Earth's oceans, creating two tidal bulges. One bulge forms on the side facing the satellite and the second appears on the opposite side of the planet because gravity weakens with distance.
Isaac Newton published his explanation of tides in the Principia in 1687. This work established that the gravitation of the Moon caused the tides.
Measurements made in November 1998 at Burntcoat Head in the Bay of Fundy recorded a maximum range of 53 feet. The Bay of Fundy has the world's highest tides due to its shape and bathymetry.
Careful Fourier data analysis over a nineteen-year period uses frequencies called tidal harmonic constituents. Nineteen years is preferred because relative positions repeat almost exactly in the Metonic cycle.
La Rance at Saint Malo, France is the most famous installed system. Impoundment dams are expensive to construct and disrupt natural water cycles.