This is one of the questions that a university student has to face more frequently during spring and summer. When I travel, I like to be independent from locals (even if I’m fond of getting in touch with new people), just because I like planning things in advance.
Most of the people arrive in Pisa by train, expecially when getting to Pisa from Florence or Livorno, the port in which every love boat stops; also buses from Pisa airport (line 3) stop here at Pisa Centrale station. First of all, you’ve got different choices: you can reach the tower in a cab, by bus, or on foot. Consider the fact that reaching a place in a cab is easy, while taking a bus could be uneasy.
By Bus
Anyway, when you’re in the entrance hall of the train staion, you’ll see two newsstands; they sell also bus tickets (in Italian = BIGLIETTO, pronounced beeleettou), and you’ll need to validate one for each way on the bus. The bus stop is on the opposite side of the station (the ones you have on the side of the station are not okay), and you have to look for the "NAVETTA A". Anyway, if you have any doubt, ask the driver, saying "TORRE?"--that means "tower" in Italian. You'll need to do the same to locate the right bus stop for you because the bus stop next to the leaning tower is outside the square, so from the bus, you are not able to say if you’re near or not.
The bus stop is next to the "Santa Chiara" hospital; you’ll recognize it because there’s a red cross on a sign. In front of the hospital, there’s a service area named "AGIP". When you are here, you can drop off and look to find a big arch that leads you in Piazza dei Miracoli, where the tower is.
On Foot
I prefer this way of reaching the tower; you just have to plan a short walk of about 15 to 20 minutes, maximum. I’m accustomed to this path because I have to reach the university every morning, which is next to the tower. This way is not so "panoramic" or "breathtaking", but it is the shortest.
First of all, leave the train station, exit to the big square, and look to your left. You’ll see a cinema, a hotel named "Roseto", and a narrow street. Enter that street, go straight on, and then cross the road. You have to veer a little bit left (not turning left) to enter the other road and go straight on. You'll have the bus depot on your left. Cross the road again, and you’ll see a big square with a church and many cars parked on it. (Note: On the rear side of the church, you can reach in few minutes an enormous painting by Keith Haring).
Cross the road and go straight on, entering "Via Crispi". Walk for some minutes and reach the bridge, named Solferino. This is one of the bridges on the Arno River, the same river of Florence. When you’re on the bridge, if you look to your right, you can see the "Chiesa della Spina" and, farther away, another bridge called "Ponte di Mezzo", or in English, Middle Bridge. This bridge joins Borgo Tretto and Corso Italia.
So cross Solferino Bridge after taking some photos of this panoramic view, and go straight on for about 5 to 8 minutes. Then you’re in Piazza dei Miracoli, which is the location of the leaning tower, the dome, the monumental graveyard, and the baptistery. I’ve made a little map for you; please forgive me if I’m not so good at drawing.