Depending upon the distance between you and the source of the disturbance which is triggering the waves, you might have only minutes, but often you will have several hours.

Santa Barbara,CA experienced a horrific earthquake/tsunami in 1812. The epicenter was very close (middle of the Santa Barbara channel) and the tsunami which closely followed was disastrous. of course there was no technology available to give warning.

Other earthquake events in the pacific Basic (such as Fukoshima) will provide several hours advance notice and one will have several hours to seek higher ground. in my community there are signs designating areas subject to inundation and the county hazards map, as well as local signage, designates recommended escape routes. fortunately, there is a lot of relief in my nck of the woods. My house is about one mile from the beach, but 200 1/2 feet above sea level,so we are not greatly concerned about waves.

To deal with a locally generated tsunami, the rule is - if you feel an earthquake, seek high ground, rather than going to the beach, until information is available about the nature of the event. Not all EQs will necessarily generate a tsunami,but this cannot often be determined immediately.