I noticed a lot of questions on this topic so I thought I would share my recent experience. Upon our arrival at the airport, we had planned to take the aeroport bus downtown, but just missed it. Not wanting to wait for the next one, we took the Metro down to our accommodation near Calle Atocha and Calle Fucar (Huertas district). We bought the ticket from the machine (press the British flag if you want English). We had to change lines twice to get to our destination but it was fairly simple. However, I would not recommend this way if you have a lot of heavy luggage, as there area multiple stairs to go up. But if you are travelling light it's a great economical option.
Returning to the airport, we caught the yellow aeroport bus at Atocha station. I preferred this method as you just sat and enjoyed the scenery.
Both methods are the same price - a bargain at 2 euro per person.