Madrid is most easily accessible from New York via Iberia, with nonstop daily flights to Madrid. All other major Spanish cities can be reached via Iberia through Madrid. TWA also flies nonstop daily from New York to Madrid and has direct New York service to Barcelona through Lisbon, with some flights to other cities via Iberia.
TAP (Air Portugal) and TWA also have frequent flights to Lisbon, and Portugal is also connected by air to most European cities.
Spanish and Portuguese trains are notoriously slow--both countries still lag far behind the rapid rail connections and comfortable coaches that characterize France and Germany. Trains in Iberia rarely leave on time and you are likely to be crowded into a compartment with seven other people, sometimes with chickens and an occasional duck.
But trains provide by far the most realistic view of Iberia and the people, with a rare chance to converse with strangers. Young people wanted to talk about music--mostly rock and reggae--and about life in America. Passing cigarettes between strangers is as common a custom as handshaking. Not too infrequently hashish is passed.
Since Spanish trains are usually crowded, reservations can guarantee you won't spend 24 hours standing in a narrow corridor. Take along your own food and bottled water, since dining cars are still considered a luxury.
The best train connection is the Madrid-Paris express, the fast Puerta del Sol, which makes the run in about 15 hours.. The most scenic route, I think, is the treacherously long trip from Rome, which winds along the Mediterranean into Barcelona. This train passes through mountainous northern Italy and southern France.
Lisbon is easily reachable with daily express trains from Madrid. Portugal also has frequent trains to the north, Oporto, and south to the Algarve region. A ferry boat takes southbound train riders to the correct station.
Inexpensive pensiones (cheap hotels) literally line the streets in both Spain and Portugal, with prices as rock bottom as $3.50 for a comfortable single room with a shower down the hall. Conspicuous tourists need not worry about finding one--the local entrepreneurs crowd the train stations offering newcomers everything from a cheap room to a little under-the-table currency exchange. Tourist information is available at or near the stations in both countries.
Meals are also a bargain, especially in the popular, stand-up cafeterias. The plato del dia will likely include soup, a paella (a main course usually of seafood, chicken and rice , hard bread and a small bottle of wine, all for as low as $3 (U.S.). Menus are posted outside, so comparing prices is easy.