By train from Pisa Centrale (direction La Spezia). The price is around 8 €. There are plenty of trains everyday.
Besides enjoying the beauty of this small town, hiking the trails to the other towns is definitely worth a day or two in the area. See Cinque Terre for more information on the paths.
When you arrive at the train station, you may need to go underground to reach the main platform. Head down the tunnel toward the city. During World War 2, the residents spent the nights here for protection. There is a wonderful art gallery with oil paintings and watercolors of the cinque terre towns. Turn right and up the hill -- this road used to be a stream, with bridges crossing , similar to Venice. The stream was paved over and you can still hear the running water. About half way up, there is still an old water wheel. At the top is the church of S.Lorenzo.
Ostello Cinque Terre  is the largest hostel in the area and one of very good quality attracting people from all over the world. Includes dorm rooms with en suite bathrooms, laundry, food services, internet access, etc. It gets very busy in the high-season and they will not reserve less than a week in advance.
Unfortunately due to a political situation in Riomaggiore Ostello Cinque Terre  was forced to close and has reopened as a hotel.
One of the trails, found on the Cinque Terre section.
You can also buy a daily train ticket to move between the Cinque Terre cities and leave the area.
From Manarola you can walk or you can drive with bus to Volastra. From Volastra you have a good view to Manarola.