There are three ways to get to the Anambas Archipelago.
1. Fast ferry
You can take one of two fast ferry services that go to Anambas. One ferry departs from Bintan, whilst the other departs from Batam. Both of these Indonesian islands are about a one hour's boat crossing from Singapore. The subsequent onward journey to Anambas takes about 7-8 hours, subject to weather and sea state of course. Make sure you get your tickets in advance, because the ferry service is in demand by the locals and there's just a single crossing per day.
2. Passenger ship
You can take the Bukit Raya, a converted cargo liner, which now serves as a passenger ship, plying the sea between Tanjung Pinang and Anambas. You can get regular seat tickets and cabin tickets. Cabin tickets are a little higher, but well worth it, because the journey can be up to 20 hours. Mind you, there's plenty of entertainment on the ship, so it's actually more like a little fun cruise than a ferry crossing.
Lastly, you can fly. There are planes to Anambas from Jakarta, Batam and Bintan. The flight is about 1 hour or so and the tickets cost US$ 125,- for a one-way and US$ 250,- for a round-trip.
For the details on how to get to Anambas, click www.anambasferry.com