There are a couple of different options for travel between Pisa and Genoa; you can either travel via the Cinque Terre on a Regionale train, or take a faster InterCity route which travels along the same route but stops less frequently. The Regionale train described here runs less frequently direct to Pisa, although there are plenty of services travelling to La Spezia (around 8mins from Riomaggiore) which has plenty of onward services to Pisa. In fact, this service only once a day, and only towards Pisa. If you want to travel at any other time, or in the opposite direction, you will need to catch an InterCity service, or travel via La Spezia.
This route is operated by single decker trains (as opposed to the double decker services found on other Regionale routes). Between La Spezia and Genoa, the journey passes along the coast, stopping at the Cinque Terre (Riomaggiore).
Regionale Trains:
Italian regional train services (Regionale), operated by Trenitalia are the most basic train services in the country. As a result, they are a little scruffy, not that modern, but also surprisingly cheap. There are both first and second class options. Generally, seats are arranged in fours (sets of two facing each other). Reservations are not required, although you obviously must sit in second class if you only have a second class ticket. Carriages are sometimes air conditioned (depending on whether it is working or not!), and are generally safe, although don't be surprised to be visited by beggars on some of the more popular routes.