Micro-managing entails that you have a larger end that you're working for. Civ is for most of us only as rewarding as the amount of effort we put into it (to a point of course). Outline some goals before the game begins: the victory condition you want to win by, your foriegn policy, stuff like that. Once you get into the game, start planning ahead. This is why Civ is turn-based. Make some realistic goals for yourself for expansion, war, economy, culture etc. Know when you will hit your Golden Age to maximize its effects.
Here's an example of some basic micromanagment: say you're producing a steady stream of Swordsmen for an early conquest. They cost 30 shields each, so in the cities making them, try to work the tiles in such a way so that you yeild 5, 6, 10, 15 or 30 uncorrupted shields a turn. Even producing 11 shields a turn is a potential waste, because you could change a few labourers around to get more surplus food insteading of producing 3 unused shields. Know how many you are going to make, so you can anticipate when you're force will be ready, and when you'll stop producing units that you'll never use but might still pay for. If it isn't obvious, you cannot micromanage with automated workers.
One of the first steps you can take is making sure that no size 12 city is producing a single extra piece of food before the discovery of Sanitation. The advantage you'll have over the AI is astonishing: just one extra sheild each in 20 cities over the course of 50 turns is 1000 more sheilds, enough to buy 10 marketplaces, or add 14 more Knights to your army. The average amount of shields I find you'll garner from micromanagement is closer to 4 or 5 per city, so after 50 turns you will come up with 4000 to 5000 more shields then the AI. This is why I can't agree with you Zild, because the AI definitly needs to 'cheat' if we're going to have a challenge here. I won't turn on the goveners as an 'equalizer' because there is really no going back after getting that feeling of acomplishment. It is not more realistic because a governor would not produce enough extra food to feed 5000 people only to throw it all away.
I am by no means a hard-core mircomanager, in fact I only got into it 10 or 15 games ago (although I stopped using automated workers really early). Look around the board (JOIN THE DEMOGAME!) and you'll find people who put Diety and Sid to shame because of their admirable attention to detail. And as I said before, micromanagement is a means to an end. Do not bother micromanaging if you haven't defined your end.