Walk. The historic centre of Pisa is small — Campo dei Miracoli to the river is fifteen minutes on foot, and most of the sights are inside that loop. Trying to drive within the centre is pointless and largely forbidden.
For longer hops, bus line LAM Rossa runs every ten minutes from the station up to the Leaning Tower, with stops along the Lungarno. Tickets €1.50 from kiosks or the machine on board. Bikes are popular — several rental places in the streets around the station hire by the day for around €10. There is no metro.
Taxis can be picked up at ranks at the station, the airport, and Piazza Garibaldi by the river. Uber does not operate, but the Free Now app does.