An oil rig is an original productive building used to make money. It can only be made on each oil spot once. If you see a black dot in the water, then that is an oil spill.
An oil rig is created by bringing an oil ship to an oil spot. ( If you do not see this there may not be one or increase your graphic settings). The ship can then be turned into an oil rig via the Control Units menu. When using an oil rig, it gives you $10 per minute on each oil spot filled with one of your oil rigs, unlike energy crystals they cannot be used to make more than $10 per minute. They are mainly just used for cash due to making a base is out of the question.
The fact that it costs 35$ and produces 10$ per minute like a power plant makes it very efficient, but keep in mind the cost to build a Naval Shipyard.
When attacking a nation, it can be good to attack their currency to lower their chances from their army from growing, but it is also a good idea to defend your oil rigs in case your money per minute is low.