I've found that just managing more carefully is usually enough to give the human a decided advantage over the AI at Noble level. You should not take that to mean that Noble requires micromanagement because it doesn't. However, instead of just following the computer's advice, I've found that trying to ignore the computer and think through the situation logically is the best way to improve.
This is especially true when it comes to two things: workers and technology. One of your infrastructure goals at Noble should be to specialize cities more. In warlord, you can get a fairly decent empire running with 5-6 cities containing all or most buildings and wonders. In Noble, you really want to start thinking about focusing cities on specific things. For example, I like to have two cities used primarily for military production. As a result, they should focus on production with a lot of mines and farms. In another city, I want to emphasize gold production so I build cottages and windmills and markets and banks. In another city I want to focus on research, with libraries, universities, and observatories. In still another city, it is important to produce culture. In another, I like to focus on Great People production. National wonders help to emphasize the specialization of cities. For example, in my primary military city, I like to have Heroic Epic and West Point. In my other military city, I like to have Ironworks and Red Cross. A lot of the time, the computer does not make decisions based on how you want your empire to look. Think about what improvements and build orders help you the most instead of just relying on the computer's suggestions. After all, the AI is simply using the computer's suggestions. How are you supposed to beat the AI if you are just emulating it?
This also applies to technology. Your research should be focused. Military is obsolete? Time to go research some military techs. Don't have a religion? It's probably a good idea to go out and get one if at all possible. This is especially true when it comes to finally obtaining victory. For example, if I'm going for domination, I like to build my technology up to getting flight, assembly line and composites. For space race victories, I like to build towards the tech that allows space elevator. Feel free to skip techs that you don't need or have minimal use for in the short term. For example, in my current game, I am Bismark, and was given a good starting location on the coast by the mouth of a river with several health bonuses around. As a result, I found it possible to skip on picking up Animal Husbandry and some of the other health related resources.
I would be remiss not to mention tech trading. Tech trading becomes increasingly important as the difficulty level increases. You should not feel wary trading at a loss on Noble or above. If you have a tech for 490 beakers, it is perfectly fine trading it away for a tech you need that only required 420 beakers of research. The AI trades techs, and it is possible to find yourself technologically backwards quickly if you don't trade as well.
Expand intelligently. When you engage in war, do not simply capture and hold every city. Some of the AI cities will inherently be more valuable than others. Do not be wary of razing cities. This is especially true in early wars when you don't have the infrastructure or civics to support an expansive empire.
Leave some wonders for the AI. I remember an excellent Civ3 War Academy article that talked about the dangers of Wonder-addiction, as it is called. Make a specific goal to go for a few wonders when you have the bonuses to produce them fast, you researched the tech before most of the other civs, and it helps you. Otherwise, leave it to the ai. Many wonders won't help as much as others depending on your strategy.
Use your civics to your advantage. Don't just switch to a civic because you unlocked it. Understand how the civics change the face of your empire. To emphasize the use of specialists, it might be nice to run Representation, Caste System, Mercantilism, and Pacifism. Universal Suffrage is nice for the late-game push for a Space Race victory provided you have been building cottages. For the warmonger, running Police State, Vassalage and Theocracy seems to be a nice combination.
The last, but perhaps most important, advice I can give is this: play to the strengths of your leader, UU, and terrain. Your civ begins with two traits that give several specific advantages. Make those advantages work for you in the game. If your leader is expansive, it might be worthwhile ignoring some of those early health related resources. Furthermore, every leader begins with two free starting techs. This combination gives you a head start on two tracks in the tech tree. Translate this into your advantage. For example, if you start with mysticism, it might be a good idea to go after an early religion and spread it rapidly. Otherwise, it might be a good idea to hold off and aim at one of the later religions. Each civ also has a distinct UU. If you're playing as Rome, it might be a good idea to hurry towards Iron Working to start building Praetorians. For the Russians, get military tradition as quickly as possible. Lastly, there is terrain. You decide the map at the beginning of the game, but it, as well as your personal terrain, should have a large impact on how you play. Terra map? It might be a good idea to head off to Optics and Astronomy. Same for continents. For a Pangaea map, it isn't as crucial to pick up those two techs quickly.
So that's it. Those are the few tips, suggestions, and things I think about when I play a game. All in all, I just think that Noble requires just a little more focus than the earlier levels. Basically, that means you have to think a little more about each decision initially. After the first couple games, it becomes easier, and before you know it, Noble will be a piece of cake, and you'll be on these forums wondering how to make the jump from Noble to Prince in no time.
With that said, I'm by no means a great player. So take it as it is. Hopefully it helps.
-MM
