Casola is on the Garfagnana line between Aulla and Lucca.  The name of the railway station is Minucciano-Pieve-Casola.  To get there from Pisa, one can go via Aulla and head east along the Garfagnana line, or alternatively go via Lucca and head north-west along the Garfagnana line.  If coming from Genova or from Parma, the route is via Aulla.  Here are some Saturday train times for the Garfagnana line to and from Casola, showing also the Pisa connections.  Bold means that the train between Pisa and Aulla, or between Pisa and Casola, is direct.

Trains to Casola (via Aulla or via Lucca) Saturday 25th April 2015
dep. Pisa Centrale06:1008:4012:05  20:06
change at Aulla Lunigiana07:1710:3713:50  21:15
dep. Aulla Lunigiana08:2110:4514:0216:2019:1821:45
arr. Minucciano-Pieve-Casola08:5511:1814:3516:5319:5022:14
dep. Pisa Centrale 07:5009:5013:4315:5017:50
change at Lucca  10:17 16:17 
dep. Lucca06:0108:2511:4114:1216:2718:18
arr. Minucciano-Pieve-Casola07:3709:5813:0815:4317:4819:47
Trains from Casola (via Aulla or via Lucca) Saturday 2nd May 2015
dep. Minucciano-Pieve-Casola05:2006:0106:3607:3808:4209:5912:51
arr. Aulla Lunigiana05:5106:4007:1108:0809:1210:3013:28
change at Aulla Lunigiana06:2306:57  09:2210:3513:45
arr. Pisa Centrale07:3608:27  10:5612:0015:26
dep. Minucciano-Pieve-Casola06:3907:1408:0909:5611:1613:2914:36
arr. Lucca08:1108:4909:3411:1112:4614:5416:10
change at Lucca  09:42 13:12 16:42
arr. Pisa Centrale08:4209:1610:13 13:4315:4317:13
* Update * for people arriving on Saturday afternoon via Pisa

At Pisa there is an inconvenient gap between the 17:50 train and the 20:06, but from Aulla to Casola is 22 km (14 miles) so a time-saving alternative is to take any train from Pisa to Aulla and continue to Casola by taxi.  Here are some direct trains from Pisa to Aulla on Saturday afternoon which fill the gap:

dep. Pisa Centrale18:2219:09
arr. Aulla Lunigiana19:3120:24