Short answer
You provide a saliva sample at home, a lab extracts the DNA from cells in that saliva and reads specific points in it, and those readings are compared against research to produce your report.
Every cell in your saliva carries your full DNA. The lab extracts it and reads hundreds of thousands of specific spots, the ones research has linked to traits and health tendencies. Your pattern at those spots is compared against scientific data to generate each result. You give the sample once; because your DNA does not change, the same data can be re-read later as the science advances.