The continents rarely get pushed under each other, but the ocean floor does commonly get pushed under the continents and back down into the Earth. The Himalayas are the exception where two continents have hit and are still moving toward each other with a lot of crust getting smashed and pushed up much higher than usual. But even in this case the continental crust is not going back into the earth. It is much less dense than the rock below it and thus will "float" on top.
Reconstruction of where the plates were in the past is mostly determined by paleomagnetism (subject area of my PhD). When lava erupts and cools, it gets magnetized in the direction of the earth's magnetic field. This can be measured directly in the rocks themselves or seen as magnetic anomalies in the oceans. Since the magnetic field flips directions every 1/2 million years or so (a somewhat random process) the rocks around the ocean ridges that are spreading and erupting continuously all get magnetized in one direction and then another. This produces magnetic anomaly stripes that have been measured all over the world.
Using these ocean stripes, which can be treated like slices in time, it is quite straight forward to reconstruct what Pangea, the most recent supercontinent, looked like and where it was located when it began to break up about 175 million years ago. Almost all of the current ocean floor was created after this breakup, so before that reconstructions become much more difficult.
This a very simplified explanation. The older the rock, the less likely the original magnetization was preserved. Also, the continents have been growing slowly over the 4.5 billion history of the earth. The earth was almost all ocean at the start. The oldest rocks known are about 3.2 billion years old, so before that almost nothing is known about the magnetic field of earth (some older zircons survive in these rocks, but they are unlikely to preserve a record of the magnetic field). The wikipedia entry on plate tectonics is a decent place to start to read more about the process.
If the Earth's magnetic field flips somewhat randomly every 1/2 million years, and there is randomness in that timing, how can it be a reliable measurement mechanism at 50 million years? 500 million years? 2 billion years?
From the sea-floor anomalies, we are pretty certain that the field is mostly a dipole (magnet like) during last 160 million years. The actual magnetic field direction at any one place at a specific time will vary from the ideal dipole field by up to around 30 degrees, but over thousands of years the average field direction is that of a dipole(mostly). So, to get a good idea of the true direction of the magnetic field at a given place on a continent in the past, one would want a decent number of measurements of different ages (but not enough time to pass so that tectonic motions are significant, say less than a few million years). The more measurements the more certain one is on the accuracy of the direction and a lot of Fischer statistics are used in this determination to understand how certain one knows the true direction.
The further back we go the more unreliable and less certain we are that this is a reliable mechanism. The rocks get changed by chemical reactions or heat. The solid inner core grows, so the solid core size will change the dynamics of the field greatly. The whole mantle seems to have moved very quickly all at once durning some times, but so this was so long ago there are few rocks that have been studied that this strange possibility is still highly debated.
If someone tells you about the magnetic field of the Earth at 2 billion years, they are just stating a speculative theory. The last 160 million years, we have a pretty good idea.
Reconstruction of where the plates were in the past is mostly determined by paleomagnetism (subject area of my PhD). When lava erupts and cools, it gets magnetized in the direction of the earth's magnetic field. This can be measured directly in the rocks themselves or seen as magnetic anomalies in the oceans. Since the magnetic field flips directions every 1/2 million years or so (a somewhat random process) the rocks around the ocean ridges that are spreading and erupting continuously all get magnetized in one direction and then another. This produces magnetic anomaly stripes that have been measured all over the world.
Using these ocean stripes, which can be treated like slices in time, it is quite straight forward to reconstruct what Pangea, the most recent supercontinent, looked like and where it was located when it began to break up about 175 million years ago. Almost all of the current ocean floor was created after this breakup, so before that reconstructions become much more difficult.
This a very simplified explanation. The older the rock, the less likely the original magnetization was preserved. Also, the continents have been growing slowly over the 4.5 billion history of the earth. The earth was almost all ocean at the start. The oldest rocks known are about 3.2 billion years old, so before that almost nothing is known about the magnetic field of earth (some older zircons survive in these rocks, but they are unlikely to preserve a record of the magnetic field). The wikipedia entry on plate tectonics is a decent place to start to read more about the process.