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The wave "trough" arrives first.

In the recent Japan case, the seafloor thrust upward. When you have several cubic miles of seawater suddenly thrust upward, it has some serious momentum. When the seafloor stopped moving upward, the water itself continued to move upward due to momentum. Since the water could not really break away from the seafloor, it drew water in from the surrounding water (which had not been "thrown" upward) so this lowered the water level on either side of the thrust. Once the water in the thrust stopped moving upward (the "peak" bump), gravity caused it to slump back down, creating the wave which now has a trough on either side of it. Another aspect is that the Japanese coastline dropped, something like 8 feet in some places. If the seafloor between the coast and the epicenter of the earthquake also dropped 8 feet, that is another huge volume of water that, all of a sudden, has a lot of momentum, but this is moving downward and, therefore, creating a "trough".

On the Japanese coastline, this wave arrived about 30 minutes later. On the North American coastline (all the way across the Pacific ocean), it arrived the next day.

If the "earthquake" had happened on a floor covered with, say, ball bearings in stead of water, the ball bearings would have been launched into the air.

Hope this helps

A tsunami is usually cause by an earthquake offshore. For example, the Japan Tsunami was caused by a massive earthquake and a quick shift of a north american and pacfic plates. The pacific plate is thrusted under the north american plate. the pacific plate moves about 3 in west yearly. The fault "slipped" and thrusted the north american plate upward and the pacific plate even farther downward. The plate released a whole lot of energy and displaced water, causing the tsunami. The initial slip movement causes the rapid withdrawal of water, because the water rushes in to fill the place left by the slip. IT's like if you had a bowl of water and but a weight in it. When you withdrew the weight, water rushes in to fill the space, making the water at the edge of the bowl retreat (the rapid withdrawal), then, the water rushes back to fill the empty space at the edge of the bowl. Just imagine that on a bigger scale and continental shelves to deal with