What is the best airline to use within Spain - Barcelona to Tenerife?

Check out this airline http://www.clickair.com/view/default.aspx?lang=2 Vueling is another great budget airline here but they don't fly to Tenerife.

You can buy your tickets in advance, and I recommend doing that because, like the U.S., fares go up as you get close to the flight date. The best general site for looking up flights in Europe is http://www.edreams.com/ You can also try http://www.terminala.co.uk/webpages/index.aspx Two low-cost airlines worth checking out out: http://www.vueling.com http://www.air-europa.com/ You can also look up Spain's two big airlines, Spanair and Iberia. Notes that Tenerife has two airports, north (norte) and south (sur), so make sure you get your plans straight with which airport you are flying in and out of.

I have found that using Expedia or Travelocity from another country (like Germany) can net some pretty great deals. If you can muddle through a website in a different language, you can usually get a pretty good deal on flights within Europe. The only thing to watch is the conversion fees that your credit card might charge you to pay for something in Euros. Sometimes the fee from your credit card is so high, it eats up any discount you might get from buying from another country's website. Good luck!