https://kidshealth.org/en/parents/genetics.html and https://www.pbs.org/newshour/health/23andme-need-know should be good starts.
Sequencing the whole genome isn’t necessary because so much of it will match from just being human. They just need to check certain portions of the DNA, like seeing how a word is spelled on a book.
They’re making statistical estimations based on others’ profiles. If your set of variations matches others who report their ancestry coming from a certain part of the world, then it scores you as more likely coming from there too. If you match someone ~50% they might be a sibling, etc. And different amounts of match you can guess sharing a common ancestor however many generations back.
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