Gypsy Heart,
There are both machines (which make change) and ticket booths at the two metro stations at the airport when you can purchase your ticket.

If you arrive in Terminal 1, the metro is located between T2 and T3. The fare to Atocha will be 1 euro.
1 euro fare for within the entire Metro Madrid system.

If arriving in Terminal 4 (Iberia, BA, One World Alliance members), there is a 1 euro supplement to go from T4 to T1, so total, airport to downtown fare is 2 euros. You'll see plenty of signs in English at the T 4 station indicating that you must pay this 1 euros supplement.

Those who purchase the Tourist Pass (Abono Turístico) are exempt from this supplement. The Tourist Pass is sold for 1-2-3-5-7 days. You can see the prices here
http://tinyurl.com/336wfc

You can also buy a money saving ticket of 10 rides, a Metrobus, which is valid for the metro and busses. It costs 6.70 and can be used by your entire group. We always buy the Metrobus.

When you board the metro, put your ticket in the turnstile, it will spit it back to you. On the bus, insert it into the machine and ditto.
Just don't carry your Metrobus next to your cell phone. It will deactivate.