Is walking the best way to get around Venice, Italy
Walking, yes. But to save time covering longer distances, and to get a distinctly different view from the canals, many travelers supplement walking by using at least 2 kinds of water craft: Vaporettos, think of them as a water bus, to go longer distances. And another kind of boat, a traghetto, to cross the Grand Canal if you're not near a bridge (I think there are only 4 or 5 bridges across the Grand Canal).
Actually, I think there are only the Academia and Rialto bridges over the Grand Canal, otherwise I agree with Kent's advice. Be prepared to walk a lot and get lost. I think Venice is the only place where I have had a good map and still got lost!
Many people only notice those 2 bridges (mentioned above), but there are 3 more bridges over by the train station, that makes 5 total bridges over the Grand Canal.
There is a bridge across the canal at the train station. It is possible to walk across from there to the Frari and San Toma area. Check a map and start walking. The Rick Steves VENICE book has a decent map in the front. Finding specific addresses can be a challenge, since the numbering system for hotels and residences is a little tricky. I just ask someone when I think I am close to my destination.
The vaporetto also crisscrosses the canal, so it can be as good as a traghetto, though perhaps not as much fun. Since single vaporetto fares are very high, a pass is usually a good idea. And a lovely sightseeing trip too. Walking is a good way to get around, and also a very good way to get lost. A map and a compass are good to have, and a sense of adventure.