You can show the continents are moving trivially these days with some GPS monitoring.
The part about the lava is that when it cools, any ferromagnetic material in it, like iron, will align itself with the earth's field. Some layers of the lava have the field oriented opposite to others. The dates of the field reversals are known to some accuracy via radiometric dating, so the positions of the layers show the sea floor spreading.
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Wegener is the guy who though up plate tectonics, so doing a Google search on 'Wegener plate tectonics evidence' should get lots of info. I can't vouch for the quality of that info, though.