What is the best way to travel to Zadar, Croatia from Venice or Trieste? Have heard the train is not the best approach.

How much time do you need to make the journey? It will be nice if you can break up the trip. Provide the month--some things are seasonal, such as the ferries.
I know there are ferries to Rovinj and Pula, and then you could switch to bus.
RometoRio is the site I sue to scope out transit options when google fails. But always confirm the results with the providers it lists.

If the ferry/bus schedule doesn't work for you, another option is using the GoOpti service. We booked a transport with them from Venice to another location in Croatia and it worked well. We opted for a private transfer, but there may be a group transfer which would be more reasonable.

I agree that you should try rome2rio.com (2, not to), and definitely click through to the underlying links, as the main site is not sensitive to seasonal variation.

You might take the ferry from Venice to Istria (e.g. Pula) and rent a car there and drive to Zadar. It's a long bus ride. You could also stay over a night in Pula and fly early the next morning on a quick direct flight from Pula to Zadar, if you don't mind getting up at the crack of dawn.

I think there are also ferries from Ancona.

Winter and spring:
Train to Trieste plus bus to Rijeka - Zadar
Flixbus to Zagreb or Rijeka - Zadar
Summer:
Austrian airlines via Vienna or Lufthansa via Munich
Train to Trieste plus bus to Rijeka - Zadar
Flixbus to Zagreb or Rijeka - Zadar
Volotea flight to Split plus bus to Zadar
train Venice dp 15.25 to Ancona plus overnight ferry to Zadar ar 7am
late afternoon catamaran Venice - Pula plus morning catamaran Pula Zadar ar 13.15