Fascene Airport (NOS), about ten kilometres east of Hell-Ville, has daily flights from Antananarivo (around 90 minutes) and seasonal direct charters from Europe (Italy and France in particular). The Madagascar Airlines schedule changes frequently — check fares and timings well before relying on a connection.
The cheaper alternative is to reach the mainland village of Ankify by overnight taxi-brousse from Antananarivo via Mahajanga, then take the public ferry (about an hour) across the channel. The boat is small, the crossing can be rough, and luggage tends to get wet.
A new bridge to Nosy Be has been talked about for decades. Until it exists, plan on the ferry or the plane.