I find Anderson's original paper too terse. I am looking for something that introduces me gently to the subject so that I can understand Anderson's paper and other literature. What references are out there that introduce Anderson localization? Anything will work for me: lecture notes, review papers, introductory papers ...
I do not know much about books on Anderson localization but there was a conference some time ago celebrating the $50$ years on the proposal by Anderson in which you can find many useful references. The list is here.
I can recommend you the course by van Tiggelen. He's quite an expert in this subject and Les Houches lectures tend to be very pedagogical.
There is also a book with the same title than the workshop but a bit more recent:
The first chapter is written by P. W. Anderson himself.
In addition to what has already been said I would add:
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