The dictionary definition of looting is "to seize and carry away by force especially in war". In EU2, the spoils of war are gained simply by having an army in enemy territory. A city that has been subjected to looting becomes looted, a status which it holds for the next year.
How to Loot
Whenever an army is in an province containing an enemy-owned city at a month's end, and the city is currently unlooted, then that city gets looted. You don't have give any commands to get an army to loot, nor is it possible to have an army not loot if it can.
Any army may loot, no matter how small. It also doesn't matter whether the looting army is moving, or not, or even whether it is fleeing. Just that it is in the province at month's end. So it is easy to loot even against a superior foe, by entering the province and then immediately retreating. (Fleeing battle risks casualties and costs you warscore, of course. But cavalry almost always get away unscathed, and if you intend to eventually take control of all of the enemy's provinces to gain 100% warscore, the gain or loss from warscore in battles doesn't matter.)
Income from Looting
When a country loots a city, it gains two times the base tax value of the looted province, as monthly tax income. Unlike normal province taxes, the loot value is not modified in any way. That is, there is no effect on the loot value from your country's stability, the city's culture or religion match to your country, net revolt risk in the city, etc.
Effects of Looting on Cities
You can tell a looted city by its icon on the map: when it's looted, the icon is "smoking". Once looted, a city stays looted for the next 12 months; it can be looted again on the 13th month.
When it's looted, a city produces no province taxes or census taxes for its owning country if the owner is a human player, or if the difficulty level is very easy or easy. AI countries still get full income from looted cities they own if the difficulty level is normal, hard, or very hard. Production income is reduced for the city; a player can get some production income (but not gold) so long as the city is not covered or besieged. Players get zero gold income from looted gold provinces. A country controlling an occupied city still gets production income and gold income, even if it is looted. Trade taxes are not affected by looting.
There are other effects of a looted city: the maximum attrition level in its province is increased, by +5%. Also the population growth rate of a looted province is modified by -5% for the entire 12 months that the province "burns"; and if the loot army is not in retreat then population growth would also be additionally modified by -5% while the army is present.
If you mint in the month which you get loot, then it is turned into money in treasury, no different than any other minting. Except, of course, that the stream of income that normal minting works on is coming in smoothly over the year. There's no month that's better or worse for it. Whereas, with looting, all income comes in pulses, every 13 months. Furthermore, if you micromanage army moves correctly, you can synchronize your looting so that all of the cities which you are looting have their loot-month happen together. Then you mint just in that month, and get the entire year's income as money for just 0.0833% inflation!
Note that the owner of a city in peacetime gets its base tax value twice per year, once as money in the yearly census tax, then again spread through the year as monthly income. Since an owner gets census tax plus province_tax (which is improved by officials) in 12 months instead of 13 months, he may get more total income from the province than you do looting. Because tax values for owners are modified by stability, culture, religion, revolt risk, no land connection, etc., and census tax may be additionally reduced because of decentralization, no tax collector, or non-core status, an owner may likely get worse income from a province than a looter. If you control an enemy province, you get only a fraction of production income and no trade taxes. An owner gets full production income and also gets trade taxes; so, later in the game when infra and trade tech are high, chief judges are promoted, and the value of goods is improved it may be more lucrative on the whole to own rather than loot. But if a player needs money in the treasury, as an owner, he would have to mint for a fair fraction of a year to get as much as he can get by looting and minting 1/13 of the time!
However while the AI is minting, and much or all of that minted money can assumed to be going to you in peace reparations, the best income possible from a given set of provinces may be had by controlling, looting, and taking their income as tribute from the AI owner; this is known as AI milking.