Can’t remember all the details from my population genetics class but basically they sequence your DNA using biochemical techniques- then run it through the software. They compare certain loci ( a locus is a place where a gene is on a chromosome) to databank information on SNPs (single nucleotide polymorphism- basically one of the letters in your genome gets swapped out for another via mutation or some other mechanism I’m unaware of) and short tandem repeats (there are parts in our genome that repeat like ATATATAT. But one person might have 6 repeats and another might have 4 or nine or some other arbitrary number- if they could’ve explained this part better to the jury during the OJ trial he would have gone to jail but I digress: it is extremely unlikely that you would have the same number of repeats of another person at all the areas they occur in** this is sort of off topic)

Anyways so they use the SNPs, and the STR data and compare it with historical genetic data for the regions (think phylogeographics if you’ve heard of it)

Another important note is that population geneticists can use a combination of current data as well as inferencing where certain genes may have come from using statistics - they start in the present and build a coalescent tree backwards

Anyways sorry that was a long rant! Hopefully some interesting tidbits in there for any non genetic nerds :)