I'm afraid I've learned about them mostly by tinkering - the tool I use is: https://github.com/sarahtattersall/PIPE

I believe "Dining Philosophers" is the usual problem used to introduce the need and concept of Petri-Nets - googled for some examples I found:

http://www.cs.cmu.edu/afs/cs/academic/class/15671-f97/www/le...

Also here's the link to the PNML source used for tic-tac-toe: https://github.com/bitwrap/bitwrap-io/blob/master/bitwrap_io...