Hi,
@MickWexford and welcome to the forum!
I moved your thread out of the discussion about online Renfe sales to a new thread.
Trains from Madrid to León leave from Chamartín train station, which in in the north part of Madrid.
The easiest way to get to it from the airport depends on which terminal you will be arriving in. If you arrive on Iberia or an Iberia partner, you will land in T4. There is a Cercanías (commuter rail) stop there. It goes directly to Chamartín and take about 15 minutes.
If you land in T1, 2, or 3, it is a bit more complicated. You can get to T4, where the Cercanía stop is, on an intra-airport bus. Those buses go very regularly and take about 15-20 minutes.
The other option from T1, T2, or T3, is the Madrid Metro. It’s a great system, but the Airport to Chamartín is a bit complicated. There are several options, all reqruiring some transfers. Easiest is probably pink line to Nuevos Ministerios, change to Line 10 there. Here’s the
Metro Map.
I don’t think there is a direct bus connection either. But you can get a bus to Avenida de Américas and then transfer, I think.
Hoping you arrive in T4, since Cercanías is hands down easiest!