Introduction
Production, 
Production, is one of the most important game concepts in Civilization V. It represents how much a city is able to build each turn - be it constructing a building, or training a unit, or working on a particular project. Since all these are basic activities in the game, and start from its beginning, you can see that it's of the utmost importance to understand and develop Production in your cities.
Note that every city has at least 1 Production point from its main tile, so you can always produce something. However, if you only rely on that lone point, your projects in this city will literally take forever. Make sure you expand your Production capabilities if you want your city to progress.
Mechanics
Production is measured in points, as all other stats in the game. Each city receives a certain amount of Production points (PP) per turn, depending on all the sources of Production it has activated. Certain bonuses may apply, either permanently, or related to the city's current production project.
Similarly, all things that need to be built require a certain amount of Production points to accomplish. Once you start working on a project (building a building, training a unit, etc.) in a city, the totality of its Production PPs + any bonuses applicable are applied each turn towards completing it, and when the total amount is reached, the project is accomplished and you may start another one.
As with researching technologies, you can start and stop a project as many times as you want, then later restart it from the same point where you stopped.
There are a number of special production bonuses in the game, which apply only for certain types of projects. For example the Forge provides a Production bonus when training Land units in a city, but not for Naval units, or for building construction. The Windmill, on the other hand, applies a bonus when constructing buildings, but not when training units. Keep track of your city's potential and use it to their maximum.
- Note: If your civilization is unhappy, production in each of your cities lowers. Also, during a Golden age all cities enjoy a 20% Production increase.
Sources of production
The most important source of Production is the land. Many terrain types and relief features (such as Hills) have inherent production potential, which adds to the city total when their tiles are worked. Improvements built on the land, such as mines, increase the Production potential (although, again, that potential is useless unless worked by the 
Population Citizens in that city). Later in the game, technological development is capable of increasing even more the Production potential.
Terrains and terrain features with production potential
| Terrain | Bonus |
|---|---|
| Plains | +1 PP |
| Hills | +2 PP, regardless of terrain type |
| Forests | +1 PP. Note that you can't chop down the forest, that would alter the tile's features! |
| Atols | +1 PP |
Tile improvements that boost production
| Improvement | Bonus |
|---|---|
| Mine | +1, +2 with Chemistry |
| Lumber mill | +1, +2 with Scientific Theory |
| Pasture | +1 |
| Camp | +1 |
| Quarry | +1 |
| Oil well | +3 |
| Offshore platform | +3 |
| Manufactory | +4, +5 with Chemistry, +10 by adopting all policies in the Freedom tree |
Many Resources add to the Production potential of their tiles. The Improvements that allow access to them may also contribute to increased Production. Try to access those first, as they will give you early benefits.
Natural Resources that boost production
| Resource | Bonus |
|---|---|
| Horses | +1 |
| Stone | +1 |
| Coal | +1 |
| Marble | +2 with quarry |
| Iron | +1 |
| Oil | +1 |
| Uranium | +1 |
| Aluminum | +1 |
The second big source of Production are buildings, such as a factory. Besides providing additional PPs in your main city tile, buildings also boost total Production in a city by a percentage. And, some of them provide Engineer specialist slots, which are additional sources of Production.
Also, certain buildings are capable of adding Production to tiles worked by this city. For example, the Harbor adds 1 PP to all Sea resources worked by the city. Note that this benefit is only enjoyed if the relevant tile is worked, thought.
Buildings that provide production
| Era | Building | Production | Note |
|---|---|---|---|
| Ancient | Stone works | +1 | City must have improved marble/stone nearby, city cannot be on plains |
| Ancient | Water mill | +1 | City must be built next to a river |
| Classical | Stable | +15% when building mounted units, +1 on each horse, cow, and sheep | must have one of the previous resources near the city |
| Medieval | Forge | +15% when building land units, +1 production on improved iron | City must have improved iron nearby |
| Medieval | Workshop | +2, +10% | |
| Medieval | Harbor | +1 on sea resources worked by city | |
| Medieval | Longhouse | +2, +1 from each worked forest | replaces workshop, Iroquois building |
| Renaissance | Seaport | +1 on sea resources worked by city | |
| Renaissance | Windmill | +2, +10% when building buildings | |
| Industrial | Factory | +4, +10% | requires 1 coal |
| Modern | Hydro plant | +1 in all tiles beside rivers | requires 1 aluminum, must be built next to a river |
| Modern | Nuclear plant | +5, +15% | requires 1 uranium, no solar plant in the city |
| Modern | Solar plant | +5, +15% | must be built on or next to desert, no nuclear plant in the city |
| Modern | Spaceship Factory | +50% when building spaceship parts | requires 1 aluminum |
Wonders that provide production
| Wonder | Production | Requirement |
|---|---|---|
| Ironworks | +8 | requires a workshop in all cities |
| Temple of Artemis | +15% ranged unit production | Archery |
In addition to those, certain Natural wonders also have Production potential.
And finally, certain Social policies affect production:
Social policies that affect production
| Policy | Branch | Era | Requirements | Effect |
|---|---|---|---|---|
| Aristocracy | Tradition | none | none | +15% production when building wonders |
| Republic | Liberty | none | none | +1 Production in every City and +5% Production in cities when constructing buildings |
| Collective Rule | Liberty | none | Republic | Settler production doubled in capital |
| Warrior Code | Honor | none | none | +15% when training melee units |
| Communism | Order | Industrial | Socialism | +2 Production per City and +10% Production when constructing Buildings |
| Total War | Autocracy | Industrial | Police State, Fascism | +15% Production when building Military Units |
| Merchant Navy | Commerce | Medieval | Naval Tradition | +3 Production in all coastal Cities |
Notes:
- Adopting Piety reduces the time to build Culture buildings by 15% (vanilla Civilization 5 only)
Adopting Piety reduces the Production cost of Shrines and Temples in half- Adopting all Policies in the Order tree will grant +1 Production per city
Last, but not least, cutting down a Forest gives the nearest city an instant boost of some PPs towards whatever it's happened to be working on. You can use this strategically.
Converting Production
After researching Guilds and Education, your cities gain the ability to convert PPs into 
Gold Gold, or 
Science Science points. The city's production power (workshops, engineers, craftsmen, etc.) is loaned to either merchants, or scientists to aid them in their activities.
25% of the total Production potential of the city is then turned into respectively Gold coins, or science points. For example, if a city has 40 PP potential, it will produce 10 gold or science per turn. The process is continuous - once assigned, the city will produce gold/science until you change the Production.
Conversion is an alternate way of occupying your city with something, if you can't think of anything else useful you can build right then. Or, of course, you're desperate for some cash, or if your tech progress is turtle-speed.
Strategy
Managing Production is one of the most important parts of the game. Without Production potential, a city will take literally for ever to build even the most basic stuff (a Granary, for example). If you don't want this to happen, think ahead of time.
First, you have to keep in mind that each city has their individual features, affecting Production, and if you want to maximize its potential, you'll need to manage each city individually.
Next, you need to familiarize yourself with all game details described above, which affect Production. You can't expect a city to produce stuff fast if you haven't assigned any Citizens to work tiles with Production potential. So, start planning for that from the very start - from choosing a place to settle your city.
When doing this, think - you'll need some ways to boost production, if you don't want your city to just be a territory-enhancer. Try to settle it in an area with at least one-two Hills nearby (those are the most ready Production - providers, or with Resources which will add to Production. In the case of a Coastal city, look for Sea Resources, and try to build Harbor and Seaport ASAP (they add Production potential to resources). Regardless, you won't be able to always make cities with lots of Production potential - sometimes getting access to other Resources from the land is more important. In those cases, look to enhance Production by constructing the relevant Buildings ASAP.
Now, you'll find out in the course of the game that you don't need all of your cities to be production-monsters. In the Civilization, you build either Buildings that will enhance your stats (both in this particular city and empire-wise), or you build units and armies. Since the first is related to individual city development, and the second - not (it doesn't matter at all (mostly) where exactly units are created, as long as they ARE created), you can develop the following strategy:
- Select 2 - 3 of your cities and maximize their Production potential (assign Citizens in tiles with Production, construct the Production - related buildings). One of them should be coastal, for shipbuilding. Build the special buildings for Unit training (barracks, armory, etc.). Then train all your military or civilian units there - they'll get experience up-front, and they'll free the rest of your cities exclusively for constructing buildings for local enhancements.
If you have a city with access to Marble, you should try to make it a Production center, too, then construct all your Wonders there. They'll get the special marble boost.