From what I understand from watching specials on tidal waves is that they start out very long and not high at all. As they come to shore, the water obviously gets shallower and as a result all of this water is forced to rise up. Whoever knows more about his please chime in.
Yes -- out in the deep ocean, tsunamis are barely a ripple. When the wave motion reaches shallower water, it "humps up", because, at the risk of oversimplifying things, the wave energy has nowhere else to go but up, since it doesn't have a deep water column to resonate in.
It's just a vastly larger version of "regular" wave action. Watch the waves at the beach sometime -- they start out as low swells, then rise up and crest as they near the beach.