Take the airport express bus. It is yellow and 6 euros and drops you off at Atocha. Just go outside your terminal to where the buses are caught.
Ok... so... My flight from Dallas, Texas, arrived beautifully this time. I was walking off the plane at 8:40 am, and then through the labyrinths of T4S into the customs area. I saw and heard obvious Peregrinos around me, waiting in line for customs chatting like, "OMG, this line is long... I'm worried about (connecting flights, trains, whatever"
It's a fast line. Try to relax.
I was outside the doors at 9:40 am, after having a "breakfast" that I chose and enjoyed. But after my 15 hours of travel time I walked towards my familiar taxi stand... knowing I could suck up dollars spent (regretfully) because frankly, I didn't want to deal with complications after my hours of travel.
That's when I spotted the yellow bus!
I continued to walk towards the taxi stand until the yellow display on the side of the bus showed "ATOCHA" extremely.
At this point, I said "Why not try?" and I headed towards the bus and found the bus driver taking tickets behind a plexiglass border, which I respected, and I said, "one for Atocha" and he said, more or less, "5 Euro".
Ticket in hand I got to experience the ride. I double checked our destination using my handheld gps and mapping technology (like any phone + google maps or whatever). The bus was spot on...
I was a little disappointed with the additional stops (2 different airport terminals) and then the central city stops that apparently may be intended for museums and otherwise worthwhile things to do in Madrid. I wouldn't know.
But, looking at my phone, I realized I had plenty of time, and I just sort of enjoyed how the bus got so crowded with locals and a slight mix of visitors like me that it was maybe just a little bit uncomfortable, but with a spirit like "we're all in this together" that eased any fears.
Anyways, after departure from MAD around 9:43 I found myself safely planted in the Atocha station around 10:30... and it cost me 5 euros instead of 30.
Now in my room in SJPdP.
Thank you for your advice.