Vernazza ~ stop in Pisa ~ Florence public transport recommendations

Train. See the Trenitalia website for specific times. Note that you need to use the Italian place names. Eg Firenze, not Florence. If you are also asking about local transportation within each place; walking is all that's really needed if you're only hitting the main tourist spots. In Florence, there are buses if going further out.

hey hey boss lady
like CJean says, check the train schedules.

like your other post, "quickest travel" meaning how to find transportation or getting to town/village the quickest way possible?
aloha

Not all routes go through Pisa. So best bet is buy a regional ticket to Pisa and then a regional ticket on to Florence. That way you are sure of doing what you want. Buy both tickets in Vernazza but don't validate the ticket to Firenze (Florence) till you are back in the station at Pisa.