Food
The simple rule of thumb is to irrigate plains and mine grass. An additional rule is to irrigate food bonuses, such as cows.
More complex explanation:
under despotism, there is a tile-penalty. Everything citizen that produces more than 2 of something, produce one less.
So if a citizen was working a grass tile, it would produce 2 food, if you add irrigation, it would produce 3 food, but if you are in despotism, it will produce 2 food anyway.
So under despotism, irrigating grassland is a waste!
irrigating plains is not, because plains give 1 food irrigation adds 1, so its 2 food.
Irrigating flood plains is also not a waste. A flood plain has 3 food, 2 under despotism, 4 with irrigation, thus 3 under despotism.
Early on, food is power, more food means more citizens working, means more of everything, but due to despotism, irrigating everything isn't an option. So only irrigate those tiles that can break through the penalty. Such a flood plains, or whines-on-grass, or cows, or wheat, etc.
Once out of despotism, look at each city, irrigate what is needed for it to be at its max size (12 citizens need 24 food to live) and maximize shields (thus mining) without letting the city starve.
The highly corrupt cities, far away from your capital, only need irrigation, food is never lost to corruption. Use the surplus food to support specialist, preferably scientist.
Commerce.
A road adds +1 commerce to the tile it is on, make sure every citizen is working a roaded tile. Especially under the republic government, as the republic bonus only works for citizens that produce at leas 1 commerce to start with.
To ensure that you have enough tiles improved, make sure you build enough workers. The no#1 mistake of new players is that they don't build enough worker units.
Also, make sure you don't build city improvements you don't need. Some rules of thumb:
Only build barracks in cities that are producing military units. (and artillery type units, such as catapults don't need them either)
Only build a granary in cities that will be used to pump out settlers or workers, not in every city.
Only build a library if the city is producing at least 10 base science.
Only build a market if the city is producing at least 10 base tax.
Only build a market if the city has at least 4 lux resources connected.
Military, its the same thing: If a city is not going to be attacked anytime soon, having a defensive unit inside is a waste of unit upkeep. One thing new players often do is put 2 spearman in every city. But if a unit is never going to see any battler, they are a waste. Better build fast moving offensive units and attack incoming hostile units before they get close to your cities. Defend your empire, not your cities.
last but not least, more cities means more of everything. So expand, expand, expand, expand. At the very least do not stop expanding untill the borders of your civ meat with the borders of other civ. And even then, declare war and keep expanding anyway.
