I get the 'childhood dream' since seeing the Leaning Tower is a must for most people. I thoroughly enjoyed see it and getting some amazing photos. Make sure you climb to the top!
We took a bus from the port to the train station. Please don't hold me to this but I believe it was the #1 bus. It took about 15 minutes. You could also take a taxi. In Italy, it's very important that you validate your train tickets BEFORE you get on the train. There are yellow machines by most tracks and throughout the station and you simply slip your ticket into the machine which will but the date/time stamp. When a conductor comes by and if you don't have your ticked validated, they have the right to give you a fairly large fine. Italians are very friendly so after you purchase your ticket, simply ask someone where to validate. Also, no need to wait in line to purchase, they ticket machines today are very modern and simple to use.
Buon Viaggio! Mark