There are several ways that a tsunami wave crest may appear to observers on the shore. The first is like a very quick rising of the tide.  The second is a large cresting wave.  The most often described appearance is called a bore.  A bore appears like a wall of approaching water that is significantly higher than the existing water level.  The image shows an example of a tidal bore in China.   Although the bore shown is not a tsunami bore, it still demonstrates the appearance and characteristics of a bore that could be generated by a tsunami. 

Tsunamis generate a wave series that may continue for many hours.  The first wave is rarely the largest in the series.  Much damage can be caused by the outflow of water back to the ocean between waves.  In some cases this reversed flow can cause more damage than the incoming waves.