Stop building wonders.
I used to be a total wonder whore. I'd try to build every single one, whether I needed it or not and regardless of who I was. I also had trouble beating Noble.Then someone suggested to me that I completely ignore wonders. Don't build any. And suddenly, the game clicked. I had more units and cities because I wasn't wasting production. My techs were more sensibly researched, as I wasn't aiming for wonders. Overall, my playstyle improved dramtically - I never lost another Noble game, and it only took me half a dozen games to "crack" Prince.
Nowadays, I do build some wonders if I think they're beneficial, but completely ignoring them while I learned more about how to play Civ was the single biggest factor in improvng my play.