Venice to Vernazza by train

The trains are roughly hourly, about 6 hours long with 2 or 3 connections, and cost €45-53 per person, 2nd class. There are a few exceptions here and there, but not worth listing them all.

What route would someone use? Venice-->Milan-->Vernazza?
What other routes are there?

Venice-Florence-La Spezia-Vernazza is most common, usually about 53 euros 2nd class. You can research routes, times, fares at http://www.trenitalia.com. Click on English at the top of the page. The cheapest seems to be through Bologna/Parma/La Spezia for about 44 euros 2nd class.