carolyn,
In the same situation, I'd probably take the short train ride (about nine minutes) from La Spezia to Riomaggiore (the first Cinque Terre town) and connect with the Ferry there as the dock is more easily accessible from the train station (an easy five minutes or so). You could perhaps spend a short time exploring Riomaggiore before boarding the Ferry.
To reach the dock in Riomaggiore, you'll need to get to the plaza in front of the rail station (your train may arrive on the outside track, which means you'll have to use the tunnel to get to the plaza). Then walk through the short tunnel that parallels the tracks and to the main street. Instead of turning left to go up the main street, continue straight and down the stairs. Keep to the left and take the path that goes around the cliff. You'll pass a ticket booth where you can buy your boat ticket. Just past the ticket booth, you'll see the stairs leading down to the area where the boats dock.
One point to note is that the boats don't stop in Corniglia. If you want to visit there, you'll have to use the local trains. As Corniglia is built on top of a bluff, there are numerous stairs to reach the town. However, there is a shuttle from the station (for a small charge). One other point to note is that if you want to hike / walk any of the Sentiero Azzurro trails including the famous Via dell' Amore (Riomaggiore to Manarola), a Park Pass will be required.
You could start in Riomaggiore and finish in Monterosso at about supper time, as there are lots of nice restaurants there. After a fine hot meal, return to Pisa by train.
