Synchronized looting is a way of using looting to get the most money possible for the least inflation. The idea is to arrange to loot a large number of enemy cities all on the same month-end. In that month, and only on that month, you mint. You get all of the loot from all of the cities as money in your treasury, for a cost of just 1/12% of inflation.
How do you actually synchronize your looting? In the general case, don't worry about synchronizing loot for non-controlled enemy cities. They must be kept covered so the enemy cannot build, and so, you cannot adjust their loot month; you loot them based on when you entered them. You can afford to leave enemy cities alone only if the enemy is unable to recruit there, which is only the case in very low-value provinces; see the discussion of recruitment capacity.
Once your sieges start to complete and you control many provinces, what you do is establish a particular month that you are going to try to synchronize all looting. (This is called your "loot month".) When each siege completes, you move all armies out of the province, then wait for it to become unlooted (it stops burning). Now it can be looted again; but you want to hold off sending in an army until the loot month.
Once you've synchronized a given province with the loot-month, you can either leave an army there all year, or move your armies in and out as required for looting. Leaving an army there is easier, but it does kill the enemy population faster. (This may or may not be desirable.) It also reduces the total force you can assemble, unless you use tiny armies to loot. On the other hand, moving armies in and out to loot require a much greater level of attention to the war than many players would like.
When you have a powerful country, you can often arrange your declaration of war and invasion such that many or most (or even all) of an enemy's provinces are reached in the first month. This is worth doing (at the cost of even more MM), because it will allow you to synchronize looting immediately, even as you siege.
Note that once you start using synchronized looting, the way in which you use warfare should change. Without it, warfare is useful primarily as a means to take land, and only secondarily for money. In a typical war, you take all enemy provinces and then make peace on the terms you want. But with synchronized looting, warfare becomes a very profitable endeavor, and especially so after you have full control of the enemy. This is true regardless of whether or not you plan to take any provinces. You do not want peace quickly; instead you want to milk every war for the maximum amount of time, basically until you can no longer stand the rebellions as your war exhaustion mounts, or you resolve to start some other war and need a peace break in between in order to drop war exhaustion and build armies.