What is the quickest train route fromVenice to Monterosso in Cinque Terre?
 

and how long would it take.
Thanks for sharing your experiences re the above stretch.

In terms of the route:
Venice to Milan and then Milan to Monterosso. Be aware that you can also do it through Bologna, Florence, and Pisa (which takes longer).
The Venice-Milan-Monterosso connection is doen via Eurostar #9492 leaving at 10:25 AM and arriving Milan at 1:05 PM; departing Milan at 2:10 PM on Intercity #653 and arriving Monterosso at 4:51 PM..a total of 6 hrs 26 minutes. The Bologna-Florence-Pisa route takes a bit longer (6 hrs 51 minutes) but connections are more frequent, as are the number of changes.
You can probably easily check timings at the www.trenitalia.com website or on the GermanRail site www.bahn.de

Intrepid,
I had a similar question for a connection from Varenna to Manarola in September. Based on Trenitalia, the route seems to be through Milan on to Chiavari for a regional(#11365) to Cinque Terre. My question - the train from Milan arrives Chiavari at 14:26 and my connection on to Manarola (passing through Monterosso)leaves at 14:31, 5 minutes to make it! Am I dreaming or is that actually a possible connection?
Thanks for your experience.

My experiences making "close" train connections in Europe have been mixed and based on a couple of factors.
First, whether or not the trains are on time. Second, the distance between platforms which really depends on the size of the station, unless the two trains arrive on the same platform one after the other. Third, the amount of luggage you're carrying.
People will tell you that 4 minutes is enough to change trains in places like Germany and Switzerland but I think it still depends on the factors mentioned above. I once was supposed to have ten minutes between changes in Hannover but i arrived a few minutes late, the trains were on different platforms which necessitated going down one flight of stairs, through a rather short underground passge, and up another flight of stairs AND I was pulling a wheeled (heavy) suitcase and wearing a full backpack. Needless to say the six minutes I actually had weren't quite enough.
What to do? If all the connections are short on the route you are taking either think of taking a different route which affords more time between connections OR have in mind a backup plan, i.e., inform yourself in advance if there are later trains from the same station that you could take if you missed a connection. That said, I always try to start out early in the day so if I do miss a train I can get another one.
I suppose I probably haven't fully answred your question but then again you and I both know there are no guarantees despite what folks here may tell you. I'd have that back-up plan figured out in advance just in case.

As a follow-on re Varenna: unless you are staying IN Varenna be aware that you'll have to time your departure based on ferry connections. The ferry dock is uphill (a good ten monutes or more depending on your walking speed) from the station and taxis do not always meet the ferries but the ferry ticket office will call one for you.

Oops..sorry..meant to say that the railroad station is uphill from the ferry dock!

Intrepid,
Thanks for your quick reply. You confirmed what I'd been feeling about my travel plans -I'd better have a good backup plan! There are earlier departures that allow for better connections, but I was hoping for a leisurely morning on Lake Como before "hitting the road"! :)
I'll be staying at Hotel Olivedo in Varenna. I understand it's about a 10 minute walk from the train station, so an early departure shouldn't be too painful.
Thanks again for sharing you advice.