Barcelona to Madrid

Just go to Renfe.com, pick you date and time for travel. Pretty simple. Any good guidebook will give you the highlights to see. See steves' Spain book.

On the Renfe website I didn't see a destination in Madrid. Do you know what the station is called? I was able to see about 5 stations in Barcelona.

RENFE is the Spanish national rail agency. On their website are the best deals for advance purchase tickets. Note that their are two classes of discounted tickets: non-refundable and changeable tickets. Discounted tickets are limited and so you may not see all of them for each schedule.

The AVE is the high-speed train system and for that run, you'll want to take the AVE train.

RENFE's website is notorious for not being easy to navigate but it helps to register and you pretty much need to pay with the Paypal option. Don't bother trying to use your US credit card directly.

For Madrid, Atocha is the station you need. There are two Atocha options, choose the Puerta de Atocha option as the other one is for commuter rail service. Most AVE trains stop at the Barcelona Sants Station.

Use tripadvisor to locate an excellent article on how to purchase renfe tickets from the USA. Advance prepurchase can save significant amounts of money. However, the renfe system for making the purchase is cumberson so please take the time to do your research.
Most important point, your purchased ticket is only good for the specific time and train you buy the ticket and is not transferable. So be sure an plan accordingly for selecting your trip and stick to this agenda.
Buy a second class ticket on the AVE train as this level of service is equal to business class on airlines (seriously). I like to travel during daylight in order to enjoy the passing countryside. We arrive 45 minutes prior to departure at the train station as going through security and access to the gate is a far better, easier experience then airports.
Upon arriving in Madrid you will be lead to an exit close to a taxi stand. Your hotel is a short, less than ten minutes, cab ride. Although you would need to make a slight detour, the main floor of the rail station is an interesting sight to see.
Give thought to accepting a room in the Atlantico located on a high floor and at the rear of the building as the street noise from the Gran Via can be quite loud.

Purchase your tickets on line per the instructions of others..;print them at home and carry them with you. The AVE train leaves from the SANTS station in Barcelona. The markings in the station are abundant, but ask for assistance if needed. Present your ticket at the gate and board the train with an x ray of your luggage. Look for the car, the number and the seat will be printed on the ticket. Also scout out the snack car as you board. Luggage goes in the bin as you enter the car. 2 1/2 hours later you will be in Madrid at the ATOCHA station. Follow the instructions to the taxi stand.

have a good trip

The Man in Seat61 recommends using loco2 for buying tickets. He says its easier, with no credit card problems. Same price as Renfe

You can get good ideas about sightseeing in each city at http://www.ricksteves.com/europe/spain, but to plan out the details, it's best to get the Spain guidebook. If you choose separate city guidebooks, then the bigger one for Barcelona has more info than the pocket guide, and carrying weight is about the same.

Don't bother the train, try Vueling airline, My daughter's flight cost €42 between two cities last Friday's morning.

Except that the plane takes twice as long. And you have the hassle of security and luggage limitation. And you have to add the cost of getting to and from city center so it is really 42+?+?.

The Renfe site offers great deals on tickets if you buy a few weeks ahead. My ticket from Barcelona to Madrid, normally 125 euro, was 39 euro when I bought it about 45 days out. The train gives you the opportunity to see the countryside in a way that flying does not. And while there is a security procedure for the train it is nothing like the one at the airport. Second class (turista) seats are comparable to business class airline seats.

The only reason to fly between the two is if you are already at or going to one of the airports. The AVE high speed train is faster total time, less hassle and more convenient. And with advance purchase tickets from the RENFE website, no more and maybe less expensive (total trip cost).

Barcelona -- In two days, and in order, here is what I would prioritize: Sagrada Familia, Barri Gotic (where you can easily see the Picasso Museum, Cathedral, City Museum and the old quarter) and Gaudi sites, (perhaps Park Guell, though on a limited time frame you might include Casa Mila and he nearby Block of Discord). La Ramblas is hard to avoid and next to Barri Gotic. Eat one night in Barceloneta....walk there from Gotic. Dinner starts around 930-10. Sites might be open later than you think.

See my posting under Transportation on how to purchase on the RENFE website. Downtown to downtown via high speed train can't be beat.