Veronica,
To begin with, you'll need to know the Italian names of the stations you'll be using, as many cities have more than one. Your departure from Venice will likely be from Venezia Santa Lucia. There's only one station in Corniglia so that won't be a problem.
Part of your trip will be via express trains (Freccia or Intercity) and those have compulsory seat reservations that are specific to train, date and departure time. Even with a Railpass, be sure to board only the train listed on the reservation or you'll be subject to hefty fines which will be collected on the spot! Any segments using Regionale trains such as the Cinque Terre Express do not require reservations, so you can just use your pass for those.
The trip from Venice to Cornigila often involves changes in Florence and either Sarzana, Levanto or La Spezia. Travel time is about 5H:45M. If the change is in Levanto, you'll actually be going past Corniglia and then backtracking.
In addition to the Trenitalia website, I believe you can also buy reservations at www.trainline.eu at the same price as charged by the rail network.
When you arrive in Corniglia you'll want to use the shuttle bus from the station up to the town (there's a small charge for that). Trust me, you don't want to be climbing hundreds of stairs hauling your luggage!