What is the easiest and cheapest way to get from the Barcelona airport to the hotel
City transport service. A bus.
The Aeroporto bus from airport to downtown leaves frequently and costs 5,30 euro. It travels along Gran Via de Cort Catalan, from Placa dEspana to Universitat to Place Catalunya. If your hotel is near that route or Placa Catalunya that is a great way to go.
Specifically, it is the Aerobus http://www.aerobusbcn.com/ Easy to find in the airport, pay driver. Drops you off at Placa Catalunya, across from El Corte Ingles (dept. store) and close to metro stop. Keep your wits about you when you get off the bus, it's pickpocket heaven (but not dangerous - just be aware).
The easiest way: By taxi, door-to-door, but also the most expensive way.
The cheapest way: 5.30 Euros with AeroBus from Airport Terminals (T1 or T2) to Plaça de Catalunya. From there you can walk, take a taxi, or the metro to your hotel. Keep in mind the easiest ways in life are never the cheapest ways. Just the opposite. Enjoy Barcelona! Saludos, BarcelonaMan @ you-know-where!!!