There are direct flights to major city's in Spain from various U.S. cities. If you cant fly directly into Spain, there are many low-cost European airlines who fly into most cities in Spain. For example, if you are leaving from LAX, there is no direct flight, so you can either fly from LAX to London, Paris, Munich or Zurich, and then catch a flight to most Spanish cities from there.
From the west coast you can also fly into the east coast, to cities such as: New York, Dallas, Chicago or Atlanta, from there you can fly into Madrid or Barcelona. If your final destination from Madrid or Barcelona is another city, you can either take a short distance flight with a local airliner, or you could go via train.
Usually the more layovers, the cheaper the price, but if you live in the East coast, you can fly directly into Madrid or Barcelona in 1 flight. There is a flight from JFK to Valencia, but its only available during the summer months. For most West coasters, they have to do at least (1) layover to get to Spain, as there are no direct-flights to Spain at this time.
The Madrid airport "Barajas" has just been renovated and is one of the most organized airports in the world. It has beautiful bamboo ceilings and window walls so you can view the outside. There is almost no airplane noise which makes the atmosphere very relaxed, with plenty of shopping, restaurants and coffee shops. Other major airports in cities like: Barcelona, Malaga, Sevilla and Valencia, offer up-dated airports, that offer an organized and pleasurable travel experience, with super-clean marble flooring, and plenty of restaurants, shops and well-organized terminals, as well as great customer service.
If you are booking your airline tickets online, you will get the best deal to Spain. If you are working with a travel agent, they will take care of all your flights and layovers to make sure you are not spending 8 hours in an airport waiting for your next flight. In summary, booking online will get you the better deal, booking through a travel agent, will get you a better flight.