Commerce sources
Commerce comes from two things:
- worked tiles
- traderoutes
In case commerce is the main supporting pillar of your economy, you generally run Cottage Economy because non-cottage improvements and resources are limited in their quantity (resources) or low in commerce yield (non-cottage improvements, unimproved tiles - eg. financial + coastal tile).
If your commerce comes mainly from traderoutes, it's unlikely to be sole basis for an economy. You might be running hybrid, trade, or other economy that uses trade commerce as secondary source or minor source.
It's important to understand that some economy types do not rely on working many tiles - eg. specialist economy might rely on working only a few high food tiles per city, then running specialists with rest. When economy is based on high food surplus, hammers may also be gained easily with the whip. Cottage-based economy relies almost wholly on working tiles. Generally the food surplus is low (except in city or cities specifically designated for running specialists - aka GP Farm(s)) and whipping is thus more painful. Also have to remember that cottages grow when they're worked, and citizens whipped away mean some cottages not worked, thus not growing either. Hammers are most likely also gained by working tiles: mines, workshops, watermills... This is incompatible with the cottages, so separation of commerce cities and production cities is more defined than in food-based economies.
Beaker sources
I would divide beaker sources as:
- commerce (slider)
- specialists
- settled great people
- lightbulbing
- buildings
- from other players (whether by trading, begging, demanding, or accepting for peace)
- stealing
Commerce slider - See sources of commerce above. Probable economy here is cottage based, but trade economy is possible alternative.
Specialists (usually combination of scientists and merchants in separate cities) are efficient beaker source under Representation civic. Without rep they're questionable, as cottages easily surpass them in beaker generation. There are other benefits from food + specialist based economies though, so that alone isn't enough to dismiss this. Generally building Pyramids to enable early representation makes this choice more efficient.
Great People require either wonders or specialists or both. Most commonly they're used to lightbulb technologies or use their special abilities. Settling GPs has been debated every now and then, and some economies (eg. Obsoletes wonderspam) specifically settle great people.
Lightbulbing is (almost?) essential at highest levels of play. There are usually two basic purposes:
- beelining (eg. bulbing Philosophy, Paper, and Education with total of 4 GSes for Liberalism)
- trading (an expensive monopoly tech traded to multiple civs, possibly newly gained techs further traded)
The former (beeline) still ends with trading of the techs, when access to them by AI civs no longer presents immediate threat to the player (eg. trade Philo + Paper when you have Edu researched, trade Edu when you're near to completing Lib). So lightbulbing as form of economy relies on getting tradeable technologies.
Buildings are unlikely source for beakers. In basic game only buildings of state religion can generate beakers, even then requiring University of Sankore - a world wonder available with Paper. At 2bpt per building a temple + monastery combination (cathedrals are big to build and you can't build them to every city anyway) comes to 4bpt total - a drop in the bucket when we consider research per city normally expected, so this is mainly side effect of the wonder or part of a religious strategy.
Other players
Trading is most common. Trading itself is not an economy, as it requires something to trade to the AI. It has been shown that buying technologies for gold is viable, but more commonly technologies are traded for other techs, and thus to get a tech in trade you have to get techs from some other source to offer in trade.
Begging (aka asking another player to spare a tech for a good friend, requires pleased or better relations) won't go far by itself. Occasionally you get something, but a couple of gold is more likely than a tech.
Demanding (at relations lower than pleased) is similar to begging. Techs aren't easy to come by.
Peace treaties are often made with one player (usually not human player) giving something for the peace. Asking for techs in the treaty is common, but in cIV the AI may easily be willing to suffer ultimate defeat before giving in.
Stealing techs is less efficient than researching them unless EPs are available by means other than espionage slider / spy specialists. Essentially this means Great Spies and infiltration. See eg. Sumerian Spy Scam thread for more about this - based on my tries to use infiltration and stealing as main beaker source as outlined in SSS thread I'd dismiss this as inefficient method on at least levels I play on (Prince and Monarch).
... and then there's the gold sources list but I'm bailing out now.