Hi Calvo....us Pennsylvanians have got to stick together.
Unless you know center city Madrid well by car, I don�t recommend driving there. It will just put you in a bad mood and you won�t enjoy the Plaza Mayor as much.
Getting to Madrid from Guadarrama is rather easy. Follow the N-VI (it is the main road that runs through the center of town) south towards Madrid. This will eventually change into the A-6 as you pass Villalba. From Villalba you have about a 30-40 minute ride to Madrid.
As you near the city, you will see that the highway splits. Keep to your right (but not your far right) and follow the signs for the M-30. The highway splits first two ways: Moncloa (the left lanes) and M-30/Sinesio Delgado (the right lanes).
After the highway divides, keep to your left of the right lanes (I believe there are two lanes). You will see that the left then splits again for the M-30 (north/east part of the beltway) or for Sinesio Delgado. (The far right lane is also the M-30 but runs south/west part of the beltway). Follow Sinesio Delgado (the right of the two lanes). This road winds around a bit, just stay on it and it will dump you right at the Plaza Castilla which is adjacent to Chamartin. If you see a parking spot, grab it and simply hop on the Metro at Plaza Castilla to Sol and from Sol walk to the Plaza Mayor.
Have a great trip and happy driving!
P.S. If my garbled directions didn�t make sense, drop me an email and I will try to clarify them for you.
Having the "car allergy in Madrid" that I do, I do not know how to get from Gaudarrama to Chamart�n. Try doing a route calculation at 
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