Most of it is reconstructed linguistically. Basically all Indo-European languages have certain commonalities, and by investigating those, scholars can come up with plausible details about the culture(s) that spoke the original language they descend from.
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This is then supported by things like the archaeological record, but it is all very hypothetical, and many details continue to be debated. Certain words and concepts though are too similar to be chance alone, so we know there's a common origin.
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There's also genetic evidence that indicates the presence of various ancestral populations living on the Eurasian steppe at about the right time, whose likely cultures are plausible candidates for the languages' original speakers. So there's a few different strands of research.
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