Several excellent introductory books on NNs are listed in part 4 of the FAQ
under "Books and articles about Neural Networks?" If you want a book with
minimal math, see "The best introductory book for business executives." 

Dr. Leslie Smith has a brief on-line introduction to NNs with examples and
diagrams at http://www.cs.stir.ac.uk/~lss/NNIntro/InvSlides.html. 

If you are a Java enthusiast, see Jochen Fröhlich's diploma at 
http://rfhs8012.fh-regensburg.de/~saj39122/jfroehl/diplom/e-index.html

For a more detailed introduction, see Donald Tveter's excellent
Backpropagator's Review at http://www.dontveter.com/bpr/bpr.html or 
http://gannoo.uce.ac.uk/bpr/bpr.html, which contains both answers to
additional FAQs and an annotated neural net bibliography emphasizing on-line
articles. 

StatSoft Inc. has an on-line Electronic Statistics Textbook, at 
http://www.statsoft.com/textbook/stathome.html that includes a chapter on
neural nets as well as many statistical topics relevant to neural nets.