War taxes are a special surcharge to province taxation available only when a country is at war. They can drastically increase province tax collection, and things based on it including census taxes and build capacity. However they come at a very steep price.
Imposing War Taxes
To impose war taxes, first you must be at war. Your stability must be -2 or higher. Then you can open the budget screen, and you'll see the "Raise War Taxes" button is enabled. Click it and there you are.
Effects of War Taxes
War taxes increase the province tax multiplier by +150%, typically more than doubling the amount of province tax collected. They affect the census tax, which is based on the province tax, similarly. However, war taxes last for only 6 months, therefore you should always initiate them in the second half of the year (July 1 through December 30) so as to benefit from the enhanced census tax. The increase in the province tax multiplier also affects the recruitment capacity of cities, allowing most cities to build more troops than without war taxes.
There are two big downsides to war taxes. First, each time you invoke them you get 1% inflation. This is a ruinous price until you have governors. Second, each use of war taxes immediately increases the country's war exhaustion by 1%, and also adds a point of revolt risk to its cities during the 6 months that the war taxes are active.
In general, paying 1% inflation is too much for almost anything. Remember that until you get governors, that's 1% of all your income, forever, that you're losing. However, there are two specific circumstances I recommend war taxes.
The first is in situations where scripted events have imposed extremely high revolt risk on your country. In such circumstances, because recruitment capacity is based on province tax levels, it's possible for you to have zero build capacity, in every city. With war taxes, you can at least build troops.
The second situation is after you have promoted governors, and are in the enviable situation of having inflation under control. Rather than have governors do nothing (or risking getting a deflation event that does nothing), it's better to hug the 5% inflation level by imposing war taxes every so often. This increases your income only somewhat (production and trade each should be producing much more than province tax). But it's pretty much free.