To find flights, start with Kayak http://www.kayak.com/flights or Matrix ITA http://matrix.itasoftware.com/. Select "multi city" rather than "one way" or "round trip." Put in Vancouver to Venice as your first leg and Rome to Vancouver as your second leg, and see what comes up. This will show you all the options.
This way, all your flights will be on one ticket. The airline is then responsible for getting you to your destination if one flight is delayed. If you book separate tickets (say from Vancouver to Amsterdam, then a separate ticket from Amsterdam to Venice), you are responsible, both logistically and financially, if you miss the connection due to a delay.
Ken has given you great advice about a route within Italy, and about connecting the cities. One refinement: a taxi from the center of Rome to the airport is a fixed rate (last time I checked it was €48), and tipping is not expected. For several people, and/or early in the morning, and/or if you have a fair amount of luggage, that's money well spent, particularly since the Leonardo Express train is €14 per person, and you still have to get to the train station to take it.