There are large data centers that 'mine' for bitcoins. Solving mathematical problems generates them and the more computing power you have, the faster you can generate coins. That's why there are these large server halls where companies generate currency. It's sort of like mining for gold, the rate at which coins are produced is deterministic.
As a person you go to a special exchange office and change your dollars to coins. Then the whole thing is done by QR codes and stuff.