how to get from Madrid to St. Jean Pied du Port

Vered, there are no trains directly between Spain and France.
You have a couple of options - depending on what time you arrive in Madrid.

1) Renfe train from Madrid to Hendaye - 8h05 or 16h15 (5 hours) - then SNCF train to St Jean
2) Renfe train or ALSA bus from Madrid to Pamplona. (3hrs)
There are 4 trains during the day (7h35 10h35 17h15 19h35) and and at least 10 busses between 8am and 9:30pm. Then Express Burricott taxi service to St Jean. Or, a bus to Roncesvalles at 6pm and a taxi to St Jean from there. Book a seat: apcaroline@hotmail.com
There is a Renfe office in the airport. It is on the lower level, just to the right when you exit customs. They can sell you a ticket there. Then you can take the Metro to Chamartin.
The ALSA buses leave from Avenida de America bus station.
If you intend walking the route Napoleon, you might want to consider booking a bed at Orisson - about 10km up the hill - so that you have a shorter first day. http://www.refuge-orisson.com/

sillydoll said:

... Then you can take the Metro to Chamartin.

Click to expand...

That is if you're going to Hendaya. If you choose Pamplona, the train leaves from Atocha in lieu of Chamartin.

Clarified,
Jean-Marc