2 days to see Madrid. I can fly for $200 in 1 1/2 hrs. Will I have to pay to check baggage on aircraft? What about the trainfare. I know it's 3 1/2 hours, but aren't there cheap fares available and how do I get them. We're arriving on 9/2. Thanks,
The train only takes 2.5 hours. By the time you add time for travel to and from each airport, and security/wait time, the train is faster. You can get the discounted fares (47 euros and as low as 35 euros for some trains) by booking on Renfe.com 62 days in advance. Some people have trouble with Renfe but we did not. There are detailed instructions on Tripadvisor (the Madrid forum page) but the most important step is to register your card with Verified by Visa AND call your bank ahead of time to advise that you will be making a foreign purchase so they don't decline the charge.
Unless you are already at the airport, the train is most convenient and faster. Often cheaper too. The costs for baggage depends on the airline and how much you are carrying. Check the airline's baggage policy. They are usually strictly enforced in Europe.