If you arrive at Pisa Airport ( PSA - Galilei Airport ) depend if you have
have extremely heavy luggages or not.
If you have a lot of cumbersome luggages you may think to get the peoplemover to the station, it is on the opposite side of arrivals than the arrivals , it will cost you 2.60€ (including luggage) but overall is not faster than walking to railway station.
If you can walk freely is cheaper and usually faster walk, quickest way is exiting immediately from airport, go north across the parking P3 , pass in the underpass under the highway (possibly stay on left), continue north on via dell'aeroporto, after about 600 m turn left into via Montanelli, at end right in via S.Agostino, then left into via dei Cappuccini and via Quarantola and after about 300 m on the right you have the back entrance of rail station.
Get a train to Firenze (about every 25 minutes, 8.60€) . According arrival time get out of train at Firenze Rifredi or Firenze SMN, following the indications on the page of arrival by train. Train ticket from Pisa is still valid to continue to my home, but ONLY by train.