Which way does a black hole spin? As far as I understand, and from what I have been shown in renderings of black holes, they spin (like water going down a drain).


*

*My question is, firstly, does the matter being pulled into a black
hole spin?

*And secondly, do they spin clockwise or counter clockwise, and why?

 A: Yes, matter falling into a rotating black hole starts revolving around the black hole. In the vicinity of any rotating body there is a rotation of spacetime known as frame dragging. The effect is only large for very heavy and dense objects like black holes, but in fact it can be measured for objects in Earth orbit. The experiment was done with the LAGEOS satellite, though I believe there is some controversy about the results. For black holes there is a region outside the event horizon called the ergosphere where the frame dragging effect is so strong that it's impossible to resist (without moving faster than light).
It isn't possible to say whether any object is spinning clockwise or counterclockwise because it depends on how you look at the object. For example if you look at the Earth from a point above the North Pole you'll see it moving counterclockwise, but if you look from a point above the South Pole you'll see it moving clockwise. Since there isn't any way to determine which of a spinning black holes poles are North and South there isn't any way to specify what direction it's spinning in.
A: Black holes spin in the same direction as the matter that created them. 
Most matter is spinning in some way. It could be travelling around the star that is collapsing into a black hole, or it could be spinning around the centre of the galaxy. Typically the matter is spinning the same way as the hole, in which case, as the matter falls in, it speeds up the rotation of the hole. If the infalling matter is moving opposite to the hole's spin, it will slow down the rotation of the hole. 
As for clockwise or counter-clockwise, there is no difference between the two. If a black hole spins clockwise when seen from "above", then it will (simultaneously) spin counter-clockwise when seen from "below".
