Spain has used the euro since 2002, which it replaced the old peseta. It is the same currency that is used in much of Western Europe. The euro is the only currency accepted in Spain, and it is unlikely you'll be able to use anything else, even in the airport. It may be possible to exchange old Spanish peseta notes in a bank, but the easiest way to get Euros is to use an ATM. Most ATMs in Spain take foreign cards, including VISA, Cirrus, Citibank, and American Express.
ATMs always give you a better exchange rate than a bureau de change; it should be the same as your bank back home, plus a small fee. And never, ever get money exchanged at the airport as you will be getting the worst exchange rate and the highest fees.
Traveler's checks were once the safest and easiest way to bring money with you on vacation. The need to show ID when exchanging them for cash and the ability to cancel them if stolen meant they were a risk-free way to travel with large amounts of money. However, traveler's checks are no longer as convenient as ATMs and other modern methods of withdrawing money.
Most traveler's checks can still be exchanged in Spain. But the only shops that will accept them are El Corte Ingles. If you need to exchange checks for money, you'll need to do so at a bank or a bureau de change.
The lines in Spanish banks can often be quite long, and their opening hours are short. In addition, there will often be a fee for exchanging traveler's checks for cash. With ATMs being so available and easy to use, traveler's checks are usually more hassle than they're worth.