Now that I know that we can see Cinque Terre in one day, I would like advise on a few things. Which town should we park at, (we rented a car)? Once we're there, should we travel between the further towns by boat or train? Thank you so much!
Parking is tough at the CT. Tourist cars are not permitted in the towns. There are two pay parking lots. One at Riomaggiore and one at Monterosso. During the high season, they are full and they sometimes block access to the road. Check out www.cinqueterreonline.com. Click on Travel Tips and scroll down to "parking". You should be able to park in La Spezia or in towns north of the CT. There is a ferry that goes from Monterosso to Portovenere that stops in most of the 5 towns. The best way to travel between the towns is the train.
Our problem with the boat was that we couldn't find a schedule. The one time we took the boat we just went to the "desk" (table) at the harbor in Vernazza and bought tickets for the next boat (which works fine as long as you have time to wait for the next boat). It is not hard to get the train schedule for the day, so trains are easier to plan. Be aware that the train station in Corniglia is not really in the town; you need to walk up or take the shuttle bus.
To do what you want to do in one day, you're probably going to need the greater flexibility of the CT trains rather than boats.