Read the tips I and others have been posting in the forum titled "The War Room". This will give you strategic and tactical tips.
Then, play against the computer. The interface may trip you up at first, but it doesn't take too long to learn the important stuff. Some of the more esoteric stuff will come later, with practice.
Finally, get into a game with humans, but make it a "tutorial game". In other words, the people aren't interested so much in winning as they are in showing how to play.
This is easily one of the most complex games ever created. Expert players still have to go to the rulebooks for answers. Games like Star Fleet Battles had a lot more rulebooks, and seeming complexity, but it was all the same stuff using different words. In EiA, every rule stands by itself as well as with the others. Even ASL would be hard-pressed to call itself more complex, although, it would be close.
You're going to find that the order of elements of the phases, and of the phases themselves, really does matter. Diplomacy is a critical element. Now, EiANW is "dumbed down" from the original board game, simple because it's not yet possible to write computer games this complex. But, it still retains a huge part of the complexity that makes players who like turn into players who love it.
NOBODY who plays this game for the first time against experienced players has a chance of winning, if the experienced players are in it for a "win at all costs" mentality. But, if you can find players willing to help rather than attack for that first game, you will learn a lot.
I do not believe a tutorial can come anywhere close to teaching this game. At best, it can mirror what playing against the AI does now: Provide an opponent to do a few things. You really want a human "tutor" rather than a computer tutorial. IMO.
At LAST! The greatest campaign board game of all time is finally available for the PC. Can my old heart stand the strain?