First step, turn off the city governors. Go to a city view and press "G". Turn off governers for all cities.
Every turn, use the domestic advisor (F1) to check all cities' happiness. You need to keep as many happy people as unhappy people. If a city is on the borderline (same amount of happy and unhappy) create an entertainer.
For production, look at how many shields are being produced and how many are needed for the project. If you're building a warrior that costs 10 and your city is putting out 8 shields then 3 are going to waste. Reconfigure the tiles being worked on to bring production up to 10 or down to 5. You'll often be in a position where you need to switch tiles each turn. One turn at 10, pump out a warrior but losing food. Next two turns at 5, pump out another warrior and creating surplus food.
Some cities will only ever produce 1 shield. Extra population in these cities should be put on taxes or science.
Use the military police! Despotism will keep two people from being unhappy if you have two military units garrisoned in the city. Pump out cheap warriors to fill this duty. Other governments differ. Only republic and democracy don't have military police.
Develop 1 city tile for each population, plus 2 more to give you flexibility in switching them around.
Use taxmen, scientists and entertainers liberally. If you are wasting 2 shields a turn in a city you might as well put a pop on research or income. These add up quickly. An entertainer is much cheaper than a turn of rioting.
You need to reevaluate what your population is doing when any of the following happens:
City growth (either population or city borders)
Change of science rate
Change of luxury rate
New tech being researched
Gain or loss of luxury item
Completion of tile improvement in city radius
That's all I can think of at the moment but it should keep you busy for a little while
Proper micromanagement generally increases your production by 25%, income by at least 10% and research by at least 10%.