One hands-on way of finding out more might be to get Anil Seth's MATLAB toolbox: http://users.sussex.ac.uk/~anils/aks_code.htm - the pdf there gives a reasonable tutorial and set of examples.
The summary in wikipedia is quite concise and to the point: http://en.wikipedia.org/wiki/Granger_causality
There is a more detailed and technical overview in scholarpedia: