If you want to get to Anambas in the shortest time possible, then you'll need to take the plane.
The Anambas airport is in Letung and you can fly to Letung from Batam, located just off Singapore, or from Jakarta. This flight operates Monday, Wednesday, Friday and Sunday. (If you're departing from Jakarta, just replace Batam.) Ticket cost should be around 1,500,000 Indonesian Rupiah for a one-way ticket or 3,000,000 Rupiah for a roundtrip, although it can be higher during peak season spells:
