To echo what's been said before, don't feel bad about dropping the difficulty level down a notch or two. Civ is a huge, complex game, and it's impossible to understand all of the mechanics all at once. It takes many games to learn them.
This is kind of interesting point. First three levels. Chieftain, warlord, noble (right?) are quite easy and AI doesn't get bonus. But those are damn lame levels. If you want AI to play bit better you have to go to prince (where I am, ehem
