Train to Venice.

Look up train times and prices at the Italian Railways website: http://www.trenitalia.com/
This will provide you with the best (quickest) route. Tickets bought in advance are a lot cheaper than those bought on the day. But, when you buy a ticket you commit to a specific train (date and time), same as for plane tickets. The ticket is only valid on that train, if you change your mind later, hard luck, throw the ticket away.

P.S. Cinque Terre is five towns (hence the name). You will need to specify which you are travelling from when you buy the ticket. And how are you getting to your town?

Cinque Terra is a region and not a town. So where are you leaving from - exactly? Most likely you are too late for any of the discount tickets so you best option will be to purchase at the station in the town you are leaving from. The best route for me is generally the least amount of travel time. Log into trenitalia.com to see the schedules. Pick one that fits your time frame.

rod,

At this late date since you'll be travelling in about a week, my suggestion would be to just buy the tickets at the local station when you arrive in the Cinque Terre. It's not likely you'll be able to get any of the discounted tickets now. The savings on discounted tickets only apply to the fast trains, and likely wouldn't be significant anyway. Which of the five towns will you be staying in?

There are two main routes between the C.T. and Venice, one via Milan and the other via Florence. I've found that the Florence route is often a bit quicker. Both routes require at least one change of trains (sometimes more changes). You can research the various solutions using the Trenitalia website, but you'll have to know the specific Italian names for the stations you'll be using on departure and arrival. Your departure station will be whichever C.T. town you're staying in, and your destination station will be Venezia Santa Lucia.

Using Monterosso as the departure station, one of the quickest trips will be a train departing at 09:12, arriving Venice at 14:20 (time 5H:08M, 3 changes at La Spezia Centrale, Pisa Centrale and Firenze SMN, reservations compulsory on two segments, and those will be provided with your tickets, two of the segments via Regionale so you MUST validate the tickets prior to boarding the train on the day of travel or risk hefty fines!).

For me, the best route is the one with fewest changes, even if it takes s bit longer. If the time difference is more than an hour, I might take the faster route with more changes.

Hello
We will be staying in Riomaggiore.

rod,

Thanks for the additional information. The route will be same as the one I suggested earlier, although about 10-15 minutes faster as you're starting in Riomaggiore (which is only about a 9 minute trip from La Spezia).

Have a look at the Trenitalia website for all the travel solutions.