NOTE: This services has disappeared again. The walk from the terminal (exit and turn left) to the harbor is well-marked, almost completely covered, and will take about seven minutes. Otherwise, there is private transfer available.
I was just at the Venice Marco Polo airport, and am delighted to report the return of the shuttle service (although no longer free) from the airport terminal to the docks. (The dock area is itself in the process of being revitalized and is looking very snappy, with new wooden decks, a bar, and more.) The new shuttle service consists a comfy, climatized motor coach, with space underneath to toss your luggage before boarding. It departs every ten minutes from terminal ground transportation for the two-minute ride to the docks, and vice-versa. The fare is 1 euro per person, payable as you board.