Many world class airliners have daily flights to Dubai, and it's easy to find a direct flight from London, Paris, Moscow, etc.

Flying to Dubai can be pretty expensive, since there is almost no charters going there. Nevertheless, you can find good deals if you compare flights and buy a two way ticket. Expect a price range of 550$ -1000$, taxes included, for one adult, from Europe, and 800$-1500$ from the United States. For more detailled prices, you can go to Travelocity.com or Expedia.com

Good luck!