DRJ
Hedonist
Hey guys, feel free to comment on my strategy and share your own strategies to cope with deity difficulty. I like to learn new stuff! 
----catching up on tech----
This particular strategy works well for deity difficulty. I suppose trying it on lower difficulties would suck out the fun of building lots of stuff (you don't really need) in your cities.
The strategy is called "100% tech". I don't know if it is has counter arguments I didn't think about but for me, at least, it works the best.
We all know it: deity sucks in the beginning, you start with only one city compared to the two of the AI.
The game is rejecting you to conquer a secound one fast - either because you don't have a good military to do so (because you can't afford it, perhaps?), or because you started isolated on an island and don't have a possibility to.
All the while the AI just rushes away in tech and score, plus, one or two of them doing it extraordinarily quickly.
A lot of catching up to do but then, once you finally were able to settle/catch some cities, the maintenance kicks in before you are able to pay for the cities and at the same time keeping tech slider at 100%, what can you do?
Yes, you got it, you build lesser wealth (and at currency wealth) to keep it high - at 100% (or 95%, if this goes better with some balancing situations. In the beginning it might even go down to 50% or lower with lesser wealth being generated everywhere)
Once you have a bit of economical growth because new techs allow new buildings or the population works more tiles or becomes specialists, you have to unswitch certain cities from producing lesser wealth. After they completed the important building, like a school of scribes or a river port, switch them back to produce lesser wealth and the next one can construct a building.
The strategy doesn't work well with meager wealth but anticipating (I wouldn't recommend beelining it) the tech "barter" for lesser wealth will be ok, usually you have to wait for more cities until then, anyway.
The strategy will enable you to very soon get close to the #1 AIs GNP value but your production is only playing secound league. You will need a good army backbone consisting of only few units.
Applying the "100% tech" strategy will give you the chance to catch an early religion like Shinto, will help you to reach much needed civics that lower maintenance more quickly and also help you to tech to writing (and currency) soon [important if you play start as minor civs].
At the same time you have to expand your empire very strategically.
You will not have a possibility to build new cities very soon. (I stopped at 10 cities and plan to stay there, well maybe an 11th for copper ore + marble)
Having a "fish trap" slice of good land for enemy settlers and units to rush to helps you to also pillage some parts of tech as well as additional money to untune cities for some turns.
EDIT: Once you caught up to AI in terms of tech I would change the strategy and gradually unlock the cities from producing (lesser) wealth, well maybe have 2-3 wealth producing cities, still.
Here are the screenshots:
1.) The "Fish Trap" (showing score, me 4th with 266 points, 1st has 417 points)
2.) Demographics (note the nearly even GNP although I only have maybe half the cities!)
3.) City Manager (8 of 10 cities producing lesser wealth)

----catching up on tech----
This particular strategy works well for deity difficulty. I suppose trying it on lower difficulties would suck out the fun of building lots of stuff (you don't really need) in your cities.
The strategy is called "100% tech". I don't know if it is has counter arguments I didn't think about but for me, at least, it works the best.
We all know it: deity sucks in the beginning, you start with only one city compared to the two of the AI.
The game is rejecting you to conquer a secound one fast - either because you don't have a good military to do so (because you can't afford it, perhaps?), or because you started isolated on an island and don't have a possibility to.
All the while the AI just rushes away in tech and score, plus, one or two of them doing it extraordinarily quickly.
A lot of catching up to do but then, once you finally were able to settle/catch some cities, the maintenance kicks in before you are able to pay for the cities and at the same time keeping tech slider at 100%, what can you do?
Yes, you got it, you build lesser wealth (and at currency wealth) to keep it high - at 100% (or 95%, if this goes better with some balancing situations. In the beginning it might even go down to 50% or lower with lesser wealth being generated everywhere)
Once you have a bit of economical growth because new techs allow new buildings or the population works more tiles or becomes specialists, you have to unswitch certain cities from producing lesser wealth. After they completed the important building, like a school of scribes or a river port, switch them back to produce lesser wealth and the next one can construct a building.
The strategy doesn't work well with meager wealth but anticipating (I wouldn't recommend beelining it) the tech "barter" for lesser wealth will be ok, usually you have to wait for more cities until then, anyway.
The strategy will enable you to very soon get close to the #1 AIs GNP value but your production is only playing secound league. You will need a good army backbone consisting of only few units.
Applying the "100% tech" strategy will give you the chance to catch an early religion like Shinto, will help you to reach much needed civics that lower maintenance more quickly and also help you to tech to writing (and currency) soon [important if you play start as minor civs].
At the same time you have to expand your empire very strategically.
You will not have a possibility to build new cities very soon. (I stopped at 10 cities and plan to stay there, well maybe an 11th for copper ore + marble)
Having a "fish trap" slice of good land for enemy settlers and units to rush to helps you to also pillage some parts of tech as well as additional money to untune cities for some turns.
EDIT: Once you caught up to AI in terms of tech I would change the strategy and gradually unlock the cities from producing (lesser) wealth, well maybe have 2-3 wealth producing cities, still.
Here are the screenshots:
1.) The "Fish Trap" (showing score, me 4th with 266 points, 1st has 417 points)
2.) Demographics (note the nearly even GNP although I only have maybe half the cities!)
3.) City Manager (8 of 10 cities producing lesser wealth)