If you arrive to Madrid
Take a taxi from the airport to Chamartin train station that currently has a flat rate of 30€.
If you prefer public transport, the Spanish railway company RENFE connects Madrid Barajas Airport with Chamartin train station through the local train network service Cercanías C1 line that currently has a price of 2,60 €. Click here for more information.
From there, take a high-speed train to Valladolid operated by RENFE that will last around 50 minutes.
Once in Valladolid, take a taxi to your hotel that will cost around 15 €. You will easily find taxis at the door of the train station.