i've never used public transport myself to go to a festival (have a campervan) but lots of people do for Glastonbury, and did for Bestival last year.
The key to it is being able to pack light. Lots of festivals have coach packages, or will have information on their web-sites about the public transport infrastructure.
this website is very good for asking all sorts of questions about festivals, and they have a pretty comprehensive listing of festivals too. Scaling down a bit this year but we usually try and do some smaller (and if possible local) ones.....