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There's lots of evidence of plate movements. In general, the oceanic crust is youngest at the oceanic ridges, and gets progressively older with distance from the ridges. The shapes of many continental landmasses fit together when they are brought back together in a manner that reverses the movements inferred from the pattern of ages of oceanic crust. Some, now distant, land masses share similar fossil assemblages and age and types of rock units that match spatially when landmasses are fit together. Warming and cooling of climates evidenced by fossils and other geology show some correlation with changing distance from poles. Magnetism in many rocks helps reveal former orientations of landmasses with respect to the magnetic poles. Subduction zones show evidence of melting of crust as it descends into the Earth. Earthquakes at plate boundaries suggest that relative movements of plates is occurring with either gradual or sudden slipping of crust along the boundaries. The crust has gradually moved over hotspots, resulting in a trail of volcanoes in places such as Hawaii. ... and lots more.
... oh - and since this is actually a Computer Science study area, rather than Earth Science, we should steer this subject on topic by noting that computers are essential for processing the massive quantities of data that are necessary for determining the precise location and depth of earthquakes and for assembling the other evidence of plate tectonics. ;-)
And modern earthquate detection is computrized. In fact, they have done soma amazing 3d maps! www.stuff.co.nz/the-press/news/7575541/3D-geological-map-of-Chch-one-of-first-in-world