Each Market generates a basic income of 10 Wealth per 30 seconds. The only way to increase this is by building the Porcelain Tower wonder, which triples each Market's production to 30 Wealth per 30 seconds. Researching Taxation technologies at a Temple has no effect on Market income.
When a Market is completed or destroyed/razed, a one-time bonus of 30 Wealth is granted.
Resources are always traded for Wealth. They are bought from and sold to an off-map trader rather than being sent to or taken from another player (if you want to trade resources with another player, you have to do this via the diplomacy screen). However, other players will be affected by commodity trades done at the market:
Buying a resource will drive its price up for all players.
Selling a resource will drive its price down for all players.
Market prices also fluctuate and 'normalize' over time. The little green arrow next to a price shows the trend (if the price is about to go up, down or remains stable).
Press SHIFT + click to buy/sell 500 of a resource, or ALT + click to buy as much as you can afford or sell everything you have. You can also toggle a market interface to be displayed in the resource box in the top left corner, giving quick access to market prices and trade options.
The Market has a Rally Point, where new Caravans and Merchants are sent to after completion. Place it on a city to have Caravans pick that city as the first on their trading route. Place it on a rare resource to have a Merchant move to that resource and automatically deploy itself (if possible). Shift + R resets the rally point to the building.
Planting an informer at an enemy's Market lets you see their resource levels (?) and the number of Caravans and Merchants they have. It can also reveal when a nuclear embargo will occur for that nation.