Most tsunamis are triggered when earthquakes near the seafloor displace a large amount of water. That water gets pushed out as a series of waves that move outwards in all directions.
If a major earthquake originates far off shore, you may have a couple of hours to get to safety. Out on the sea, the tsunami waves can be hundreds of miles long but no taller than a few feet and travel at the speed of a jet plane, up to 500 miles per hour. When the waves approach land, they will slow down and begin to grow in height.