How does the blockade work? I placed the privateer outside a city and clicked the button. According to Civilopedia I should be able to see the effected area, but nothing happened. So I gave it up. Should I have waited?
For a city to trade, it must have at least 1 adjacent coastal tile that is not blockaded. If all 8 adjacent tiles are either land, or blockaded, that city cannot trade.
After clicking the blockade button, select the ship again and you'll see shaded tiles. Enemy trade routes cannot pass through the shaded tiles, nor can citizens in enemy cities work these tiles. (All other civs are considered enemies to Privateer units, regardless of war status.)
By blockading near a city, if the city has no sea tiles adjacent to it's square that are "open", that city cannot have naval trade. Red X's indicate "closed" tiles next to a city, purple dots are "open" tiles. The left city of Kish cannot trade; the city is blockaded. The right city of Eridu has 2 open tiles next to it's square, can still trade, and is not blockaded. Neither city can put citizens to work on the green shaded tiles indicating the blockade.
When you blockade with a second unit, their ranges are combined. Selecting any unit that is performing a blockade will show you all squares that you have blockaded. In this arrangement the city of Eridu on the right can still trade, there is one "open" tile next to the city square. Again, none of the shaded, blockaded tiles can be worked by either city, which can potentially starve cities out.
You can blockade multiple cities from a single tile. Both cities are now fully blockaded in this picture and cannot trade by sea. (The city of Eridu on the right is blockaded and cannot trade, but does have some water tiles in it's fat cross where citizens can work on the rightmost edge of the screenshot)
You can blockade any city you are at war with using any type sea unit. Privateers have the special capability to blockade friends as well. If a city is blockaded by a Privateer, friend or foe, at the beginning of each turn you'll receive a small amount of gold. The more profitable the trade routes would be in the cities, the more gold you recieve.
Before Astronomy, you can blockade a huge number of trade routes with a single ship, since all trade has to occur along the coast. No enemy trade can pass through blockaded tiles, wherever those tiles may be. You could block all trade between blue and the civ to the right, for example, if you were at war with blue and blockaded with a single ship in the middle.
I hope this helps clear things up. And yeah... Privateers are really only useful in the game against civs less developed than you -- equal-tech civs will build a few Frigates to drive them away. Against underdeveloped civs, however, if they have a lot of coastal cities a few Privateers can completely annihilate them economically and starve their cities out. On a map with lots of coastline, beelining to Privateers could really wreak havoc.