I travelled to Venice Italy in January and it was an absolute dream. Cheap £15 Ryanair flights to get there and it almost felt like I had the place to myself.
One morning I got an early morning ferry to Burano and was blessed with snow and the thickest of fog. It wasn't until 10am or 11am that the tourists turned up. I totally recommend making the effort to get here early to have a much more magical experience.
In Venice I stayed at the We Crociferi hostel. Its not only cheap and set in a beautiful old Monastery but its right next to the ferry port which goes to Burano. Ideal if you are wondering or landed on this page with the search "how to get to Burano" :) The ferry cost 7 euros one way, a ticket can be easily purchased from ticket booths before you get on, and it takes about 45 minutes.
The ferry station is F.te Nove "A" and you can jump on the 12 towards P.sabbioni.