One of the best ways to gain a deep understanding about the city-states in Civilization V is to go for a Diplomacy victory.
Play as the Greeks for the city-state influence advantage and strong Hoplite combat unit
Select a Huge Earth map for room to grow and due to its familiarity
In order to throttle back the game’s Artificial Intelligence, play at a the Settler low level
The Marathon 1,500 game turn selection gives plenty of time to practice
Initial Game Play
The point of the initial game play is to build the civilization as quickly as possible from a single city to three or more. Since at this point it matters very little exactly where the first city is located, creating one straight off is a good first move. Set production for a Scout unit to automate exploration, and while that is being done, use the Warrior to expose the surrounding area.
If anything is uncertain or confusing, the Civilopedia will give enough information to make fairly informed decisions. Clicking on HELP brings up the Civilopedia.
Must Build the United Nations
The key to gaining a Diplomacy victory is building the United Nations. Once this is accomplished, then at least 12 votes from other civilizations and/or city-states need to be collected before the 10-turn voting limit runs out. Although a player can wait until the last few turns to gain enough city-state votes, more can be learned about city-states by working with them throughout the game.
For the rest of the game, the focus will be on gaining all the Technologies needed before building the UN. In the following sequential list of Technologies, the important techs are capitalized, and the ones required to gain an important tech are in italics.
POTTERY, techs leading up to SAILING, OPTICS, COMPASS, Education, Theology, ASTRONOMY, NAVIGATION, ARCHEOLOGY, Currency, Metal Casting, Acoustics, Civil Service, Physics, Machinery, Scientific Theory, Steel, BIOLOGY, Chivalry, Banking, Gunpowder, Chemistry, Printing Press, Military Science, Steam Power, REFRIGERATION, PENICILIN, Plastics, Radio, ECOLOGY, GLOBLIZATION, UNITED NATIONS (build Wonder).
Moving from POTTERY to SAILING can take many different routes that depend on specific early game strategies. From then on the overarching game strategy should be to construct the UNITED NATIONS as soon as possible.
Key Strategy Objectives
Obtaining votes from other civilizations is very difficult, but winning the hearts and minds of the city-states only takes a quantity of gold. The point is to produce lots of gold in the civilization and pay the city-states to become Allies with the civilization. The big advantage of playing the Greeks has to do with a slower decline of Influence over the city-states. They will be Allies for more turns as a result.
In return for hard-earned gold, the city-states will share their resources with the civilization. If one or more of the cities in the civilization demands, for example, cotton, becoming an Ally with a city-state that has cotton resources will satisfy the desire and cause an uptick in population growth.
Militaristic city-states will occasionally produce combat units for the Allied civilization. This can be an efficient way for defending the civilization without putting direct production into the combat units.
Pay attention to what other specialties the city-states have. They can be used to bolster other points, such as for Social Policy selections. This key objective involves learning how to use city-states in strategies other than for winning the Diplomatic victory.
Peripheral Strategy Objectives
Occasionally a city-state will ask for a specific Wonder to be built. This will bring in all the advantages of the Wonder and increase the influence over the city-state, thereby saving gold.
City-states will also ask for specific kinds of Great People. The production of Great People can be increased by means of Social Policies, Wonders and playing around with the manual settings for particular cities. Overall, keeping the city-states on the side of the civilization will enhance many other playing skills.
If other civilizations seem to be going for a Diplomacy victory, enough gold given to the city-states in contention can steal them away from the competition. City-states have no particular loyalties. They are loyal to whomever offers the most gold.
Offering to defend the city-states will increase influence. Giving them gifts of units will also do this.