Building on Frank's comments, you are talking about 3 areas: Barcelona and around, Madrid and around, and Andalusia. In 11 days, you can do a whirlwind visit to all three, or you can pick two and see them a bit more leisurely, or pick one and do it in depth. Which of these three options you choose will depend on what you want out of the trip.
For a first Spain visit, I'd choose the middle course (two of the three). If one of the areas is Madrid, you would get to the others by train. If you're not seeing Madrid, it's probably easier to fly from Seville or Granada to Barcelona.
Given Spain's size, be sure to fly from the US to where you want to be; don't fly in and out of Madrid unless that is both a logical start and a logical end to your trip. For instance, if you're seeing Barcelona and the south, fly into Seville, take the train or bus to Granada, fly to Barcelona, and fly home from Barcelona. Use the "multi city" option on airline booking sites to find these flights; don't look for two one-way tickets, as that's usually much more expensive.
To find train schedules within Spain, use RENFE (Spanish national rail) http://www.renfe.com/ or Bahn (German rail, useful for all of Europe) http://reiseauskunft.bahn.de/bin/query.exe/en. Here's Rick's tutorial on using the Bahn website: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules
To book Spanish trains in advance at a discount, there are tutorials from The Man In Seat 61 http://www.seat61.com/Spain-trains.htm#How_to_buy_train_tickets_for_Spain and from TripAdvisor http://tinyurl.com/cu48wk5. Others have reported that it's not so simple, but the savings can be substantial and so are worth some hassle.
To find flights within Spain, use Skyscanner: http://www.skyscanner.com/
Others will have to help you with where to find bus schedules. But know that buses in Spain are much nicer than Greyhound in the US, and are perfectly fine to use; they often go where trains don't, and can be more convenient when trains would require connections but buses go direct.