From San Sebastian, although the distance is small, you actually need to take two different trains and a bus to get to St. Jean Pied-de-Port. The train from San Sebastian is a local train, small with a couple dozen stops before the final destination of Hendaye, a small French town just over the border. You will need a ticket to both enter and leave the train, so keep it handy as you arrive in Hendaye. There are also a couple of border police checking ids as you leave the platform, so keep that accessible also. The price for the ticket depends on where in San Sebastian you start, but is around 2.5 euros.
The second train is more spacious, has fewer stops, and is a smoother ride, but will also cost a bit more (just under 16 euros). If you have the time between trains, take a walk around the town of Hendaye. It is a lovely seacoast town, with a family friendly beach and lovely shops and cafes. There is a craft burger place on top of the hill, that has a wonderful chef who speaks English and loves to whistle as he cooks. The locals are surfers, and some shop owners will actually close their shops for a couple of hours if the waves are right. If time is not on your side, there is a pizza machine about a 3-4 minute walk to the left, as your walk out of the train station. It will make a variety of pizzas for 8 or 9 euros, in three minutes, 24 hours a day.
Sit on the opposite side of the train from the door you enter, as this is the side the ocean is on, and will lend to some pretty fantastic vistas as you pull in and out of each town. The ride is short to Bayonne, only about 45 minutes, so keep an eye out. It is only about the 5thor 6thstop, just after Biarritz. Leaving the train station, turn right and walk a couple blocks. The buses pick up from the street; look for the one marked with St Jean Pied-de-Port in the window. If you have only a little time, there is a small art museum that is free to enter only a block from the train station. There you will also discover the river that splits the town. If you have more time, cross the bridge and visit the cathedral in Bayonne. It is easily the tallest structure around, so it's easy to find.
The bus makes 4 or 5 stops on the way to St Jean, so the driver makes the 30 or 45 minute drive in about an hour and a half. He also will drive through the town of St Jean to leave you at the bus stop. You will then need to walk back up the hill to find the old town, where all the albergues and restaurants are located. The municipal albergue is open year round and cost 10 euros. The address is 55, and the numbers increase as you walk up the hill. They lock the doors at 11:00pm, so there is plenty of time to check in. Often, there is no one working when you arrive, so you check yourself in by picking an envelope with the number of the bed on it, filling it with 10 euros, and sticking the envelope in the drop box. The town of St Jean is quite charming, and one could easily spend an entire day enjoying all the French shops and restaurants. If you are in a hurry, the Pilgrims' Office is open early and doesn't close until 10:00pm, so you can pick up your credentials and maps the same day you arrive. Buen camino!