The height of a tsunami is determined by the depth of water at the point where it starts. Tsunami wave heights of up to 50 feet have been recorded, according to Wikipedia.
The origin of the disturbance in the ocean may also influence the height of the wave. These disturbances include earthquakes, landslides, explosions, volcanic eruptions and potentially even meteorites.
The speed and the traveling distance of a tsunami also depend on the depth of the water at the point of origin. As the water becomes shallower moving toward the coast, the tsunami begins to slow down. As it slows, it increases in height. A tsunami is unrelated to normal tidal movements and is different to a storm surge, which also causes a rapid rise in coastal water levels.