Now to the point: I did everything right the first time, but I've forgotten how to duplicate it. I'm sure there's a right and a wrong way to micromanage, so I need advice on what I should generally be doing, how I should micro according to certain situations/strategies/phases of the game. I probably wouldn't be typing this if I hadn't been away from CIV for so long. I guess I just got frustrated because I had difficulty reproducing my first success. Now that I've had time to reflect, I realize I still have a lot to learn. I'm open to everything people have to say about having complete control of domestic affairs (minus BTS random events, which I don't have yet. Still playing on Warlords


).
I agree with RJ's response, as I think he goes to the underlying issue. However, you asked how to micromanage, so let me attempt to address that, with the disclaimer that I don't think it's the key to victory.
Wow. And I thought I micromanaged a lot. But there are a lot of things in that list that I barely do. I do check the graphs a little, but not nearly every turn. And I do watch my cities regularly, but not nearly every turn.
I do check the diplomatic advisor for trades every turn and I think that one is very important.
But I do use a mod (for BTS) which helps a lot with micromanagement. It for instance can tell you when your cities are going to grow or when they have grown. It can tell you that your city will become unhappy or has become unhappy. It can tell you that you can pop-rush your city. It can tell you that a foreign nation is willing to sign an open borders treaty.
If you enter a city to order a new construction and you see that you would like to poprush it next turn or maybe in 3 turns, then you don't have to remember that. You can set a reminder with text and variable duration and the game will warn you after the set number of turns.
This mod is extremely helpful in reducing the load of micromanagement. You can play as if you were checking some stuff every turn and you will never forget anything because you can set reminders for yourself. I have only told you some parts of this mod. It's called the BTS Unaltered Gameplay Mod (or shortly BUG Mod) and when you get BTS, then this mod is a must-get for any player who likes to use some micromanagement in his/her games.
Oh, by the way. Most of my own micromanagement is related to the perfect management of cities. Growing them exactly when a happiness building is finished. Finishing terrain improvements just before they are going to be used. Pop-rushing a building at just the right moment. Those things all become a lot easier with the BUG-Mod as they hardly require any micromanagement.
I also do some micromanagement with relation to re-allocating the espionage points to the various leaders (BTS- feature) and I try to not lose worker - turns by moving them around without actually doing any work. When a worker can move 6 tiles over roads, you could also move the worker 5 tiles, then order the start of a construction on that tile and immediately stop that construction again. The worker will have performed a single turn of construction on that tile and that won't be forgotten.
That doesn't sound like much, but especially at the start of the game, it's not so wise to lose worker turns. It's not a smart move to move 3 workers to a hill to build a mine there. All three will lose their movement points getting there. It's better to build a road there with one of the workers, losing only a single worker turn getting to that tile and then moving the other 2 workers along the road without losing worker turns.
I also use the draw-on-the-map feature available when you zoom out in the strategic overlay section. That and placing signs on the map allows you to plan your city placement. This is not really a micromanagement issue though. It's more an issue of detailed planning and thinking ahead.
I founded the mining corporation (can't remember exactly what it's called), and I've expanded it to a bunch of my own cities.
Each city to which I've expanded the corporation costs the new city 4 gold per turn, but gives some nice benefits (12 hammers per turn in the new city, plus 4 gold per turn in the corporation's founding city).
I understand I can also expand my corporation to foreign cities. But why would I ever want to do that?
Wouldn't that mean that the foreign city gets 12 hammers per turn? Why would I want to give them that benefit?
Even assuming my corporation's founding city (i.e., my city) gets 4 gold per turn for expanding the corporation into a foreign city, the foreign city seems to get the better part of the deal by far (the 12 hammers they'd get are much more valuable than the 4 gold I'd get). Or am I misunderstanding something?
Note that the 4 gold that you get in the Corporation Headquarters is still multiplied by the various multipliers in that city. So if the Headquarters has a market, grocer, bank and Wall Street, then you actually get 12 gold for every city with that corporation. 12 gold already sounds a lot better.
The resource gain (the 12 hammers that you mention) is completely dependent on the number of corporation resources that you have. In this case, you have a lot of them. But it's pretty likely that some of your opponents don't have a lot of resources for that corporation and thus the corporation is a lot less profitable for them. Some of them might only get 1 or 2 hammers from the corporation and you still get 12 gold in your headquarters.
Also note that the cost for corporations is actually higher than you might think. These costs are increased by your inflation and thus the cost for you and your opponents to have a corporation in one of their cities is not very low. This makes corporations far less interesting when you don't control the headquarters. The net-gain for your the opponents to whom you spread your corporations is not very high.
However, you might get some of the resources that make your corporations profitable by trading with other civilisations. These civilisations will not be so willing to trade away these resources once you spread the corporation to their cities. They will want to keep these resources to make the corporation more profitable. So you might not want to expand the corporation to the cities of civilisations with whom you're trading for valuable corporation-resources.
So when you're considering spreading a corporation to foreign civilisations, then it's wise to check who has which resources and in what numbers. You could again call that a type of micromanagement, but I would call it 'getting the right information in order to make an informed decision'.