Beating Deity is the same as beating any other level: you just have to have a strong enough grasp of the fundamentals of the game as any other level.
The main skills you need on Deity are understanding of the importance of food, shields, and commerce, and when it's best to emphasize each, understanding how to make good trades, even when you only have little income to leverage trading opportunities, and understanding the fundamentals of good early expansion. Careful management of cities, and a little micromanagement at crucial junctures helps greatly.
Can you win on Emperor convincingly? If not I suggest you step back and master Emperor first. Try playing an Emperor game where you never research technologies yourself, only buying them off others. That's good practice for Deity.
In the Succession Games forum (inside the Stories & Tales forum), I'm just finishing up playing a game called SP6: Deity Training. In it I am leading a group of players who are new to Deity to their first Deity victory. You might like to read the thread to see if you get any hints or tips.
Also, there are some good articles, especially cracker's article on opening play, and Bamspeedy's "Deity Settlers" article in the Strategy Articles forum.
Finally, you need to have tough resolve. Even if you do manage things well, you *will* fall behind on Deity. You have to have the resolve to bounce back and keep trying if you want to win.
Good luck!
-Sirp.