COLL

COLL stands for Corners and Orientation of the Last Layer.  It is a set of 40 algorithms that orient and permute corners without affecting edge orientation.  What that means is if your LL edges are already oriented and you use COLL, there is an 8/12 chance you will end with a U perm, a 2/12 chance you will end with a Z perm, a 1/12 chance you will end with an H perm, and a 1/12 chance you will skip PLL entirely.  I recommend learning it (or at least parts of it) after you have mastered OLL.  I also highly recommend learning this if you plan on learning ZBLL.  You should also definitely learn these algs if you solve with the Petrus method.

COLL is broken up into 7 orientations.  Once you determine what orientation you have, you have to recognize the corner permutation.  There are a few ways you can do this.  You can simply look at the corners and determine what needs to go where.  This is fine, but it takes too long in my opinion.  I use the "code" recognition method.  It looks hard, but it is actually rather easy.  It is a bit hard to explain though.  Basically, with every orientation there are four stickers you are going to look at, and you are going to determine the relationship those four stickers have with each other.  For example, say you had the U orientation.  In this case, you look at the ULB, URB, FUL, and FUR stickers.  The code might look something like this:
 L R F F
All this means is the ULB and URB stickers are opposite colors, and the FUL and FUR stickers are the same colors.  The letters don't literally mean "left", "right", and "front".  It is just a way to denote if the stickers are opposite colors or the same color.  Note that the code could also look like this:
 F B R R
That means the exact same thing as the grid above it.  Again, the letters are just there as a way to denote if the stickers are opposite or the same.

Hopefully that clears up some of the confusion.  If it still doesn't make sense, try setting up some of the cases and comparing the code to what the stickers are.  Hopefully it will start to click.

For the L orientation, I highly recommend learning the cases from two angles, because 3 of the 6 algs start with U2.  So the first move for those cases may or may not be necessary, depending on the angle you are doing it from.  You should also be able to recognize the Pi and H cases from any angle pretty easily.

 T U L Pi H Sune Anti-Sune