The funicular whisks you from the lower city up to Città Alta in just a couple of minutes, emerging at Piazza Mercato delle Scarpe. It's the most enjoyable way to reach the upper town — the ride itself offers good views over the rooftops below.
From the train station, take Bus 1 along Viale Vittorio Emanuele II to the funicular's lower station. Your bus ticket covers the funicular ride up. For the return trip you'll need a separate ticket, or you can walk down through the Venetian walls, which is worth doing at least once.