This is not going to be an authoritative answer for you...just my best guess from what I have picked up.
The first step was to map the human genome: "The Human Genome Project produced the first complete sequences of individual human genomes, with the first draft sequence and initial analysis being published on February 12, 2001." (per Wikipedia)
Then researchers began gathering DNA samples from all over the world, as many different populations of people as they can. Because historically, people did not travel all that far, so various ethnic groups intermarried and can be identified (with good probability) by characteristic clusters of DNA sequences, passed down through the generations.
Thus if researchers check people living on the coast of South American and find DNA sequences/clusters similar to the aboriginal people in Australia, that means you start hypothesizing how ancient Australians might have crossed the Pacific Ocean to South America!
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Likewise for evolution; something like 98% of our human genome is similar to chimpanzees, which makes it likely that humans and chimps shared a common ancestor somewhere back in time.