Getting to Pistoia is very easy since it lies on the main motorway that crosses Tuscany horizontally. In fact Pistoia is on the A11 ( commonly called Firenze Mare) motorway. From Florence it takes about 15 minutes to get to Pistoia by car, 40 minutes from Pisa.
Traffic can be hectic on the A11 motorway, traffic jams are frequent specially in the morning between 8am and 9am towards Florence and in the afternoon between 6pm and 7.30pm towards the sea.
If you travel by train from Pisa it takes about 1h 20 minutes and you have to change train in Lucca, if you come from Florence it takes about 40 minutes from the central Santa Maria Novella train station.
Bus transfers from both the airports of Pisa and Florence are available