It is highly recommendable to try to beat the masses and get to Burano as early as possible.
Rather then to book one of the tourist tours, it definitely makes more sense to use the regular public Actv boat services. They are a lot less expensive, allow earlier departures/arrivals and the freedom to stay/return whenever it suits you.
Depending on the season you can use Lines 12 or 14 to get to Burano.
Line 12 connects to Venice in the North at "F.te Nove A". Line 14 leaves from "S.Marco-S.Zaccaria A" in the South. (Go to Actv Timetables)
Note: A letter like "A" or "B" etc. means that there are several landing stages next to each other in the same place - e.g. A, B, and C.
If you intend to use more ACTV boat services ("Vaporettos") on the same day - e.g. to get around Venice and other islands - you may consider buying a 24h day pass.
Tickets can be bought at the Actv landing stages. Online purchases can be made through the AVM Venezia App. The app needs to be downloaded to your phone.
Important! DO NOT FORGET TO ACTIVATE YOUR TICKETS in your App or at the landing stage to make them valid prior to travelling!