Credits are the most easily obtained of the three resources, every fully upgraded Planet will give a certain amount per second as tribute or taxes to your empire. Enemy Culture can decrease the amount of credits you get from a particular planet, and in turn your culture can increase it. The amount gained is linked to the population of a planet, meaning Terran Planets would produce the largest amount of credits, and asteroids the least. Pirate Bases are the exception to this rule as "Plundered Booty" will produce credits like a population despite the lack of a population.
Credit gain can be increased by building Trade Ports, the longer the chain of trade ports in your trade route, the more you get. Forming Trade agreements with other empires greatly increases profit from trade. Credits are the only resource that can be used to put Bounty on enemy players to get Pirates to attack them, Pirate Cutthroats also have the "Plunder" ability that steals credits from your ships, whether this actually has any real effect is unknown, but you can tell this is being used when you see several holographic credits like in the picture on the side of this page hovering over your ship.
Credits are also the only resource that can be used to buy Metal and Crystal from the Black Market. In reverse, selling these materials can give you credits if you are short on them and have an excess in a particular resource. While some Ships, Structures, and research items may not require a particular resource, everything needs credits. There are some abilities that allow you to steal credits, including Embargo, and Plunder.