Okay, well, this is where I have to confess that despite having visited twice, I've only seen four out of the five "earths" that make up the Cinque Terre. So, this is going to based just on the first four--Riomaggiore, Manarola, Corniglia, and Vernazza. That said, the Cinque Terre are a more-crowded version of everything you hope the will be and a absolute must-visit.
The easiest way to travel between the five towns is by trail--a relatively cheap ticket (~$10, if I recall) will give you all-day access to all five, plus a code for free wifi at the stations. You do need to be wary of pick-pockets at the stations, though--I almost had my backpack unzipped by a kid here (luckily the train conductor warned us and stopped them).
There are also walking paths in between all the towns for those more fit (read: not me), but various storms have damaged them, and they may or may not be open when you go.
Riomaggiore and Manarolo are the more photogenic of the towns, and the photos that you have seen of the Cinque Terre are most likely from here. This means that they're also the most crowded towns, though, and while they are definitely worth seeing (and still my personal favorites), the more authentic-feeling towns are further down the path. Vernazza has a really lovely harbour. Corniglia is more inland (and requires quite a walk from the train up some stairs), but is a nice, much quieter place to relax and have a meal. Monterosso is supposedly where you want to go if you want some beach time, but, again, I haven't been.
Like most places I've visited, I liked the Cinque Terre more off-season. So, don't hesitate to go in the winter!