Compositing is a big topic and this page will grow in the coming months.
Compositing is done in the Node Editor window (any window in Blender can be turned into any of about 15 types including the Node Editor window). Turn on 'Use Nodes'. Now the idea is to add nodes from a selection of about twenty different types and then to connect the nodes together to achieve the desired effect. There are nodes for making images lighter, changing the color balance, combining images together etc etc. As you can see, many of these functions are the same as you might find in a graphics program such as Photoshop, even though there is nothing like the node editor window in most graphics programs.
The original images or video are input into the left side of the node setup and then pass through each node from left to right until the finished image or video is output to the right, as if the whole setup is some kind of assembly line in a factory.
There are many videos about compositing in Blender on YouTube and Vimeo. Initially I will just concentrate on one powerful example: the green screen technique:
Green screening is a very advanced video technique which in Blender would involve both the Video Sequence Editor and the compositor. Get started HERE (very good 7 minute YouTube video) HERE (30 minute Vimeo video) and HERE (20 minute Vimeo video).