If you prefer to go to the Anambas Archipelago by Bintan ferry, then you'll find all required information for a smooth unhurried journey in this website.
Your first steps towards the beautiful beaches of Anambas are by making your way to Tanjung Pinang, which is located in Pulau Bintan. Pulau Bintan is an Indonesian island, about 35 km south of Singapore. When in Singapore, you can take a ferry to Tanjung Pinang, which is about a 2 hours' sailing journey.
Now, once you're in Tanjung Pinang, you'll need to stay overnight, because the ferry to Anambas departs early in the morning. But not to worry, because there are quite a few decent hotels near the port of Tanjung Pinang and most of them are affordable.
Next morning, bright and early, head for the ferry port and hop on the ferry. The ferry goes to Tarempa, the capital of Anambas, by way of Letung, which is in Jemaja. The journey to Jemaja lasts about 6-7 hours. From Letung to Tarempa is another 2 hours or so, depending on sea and weather conditions of course.
Speaking of sea and weather, do note that weather and sea can influence the journey duration. During windy days, the sea gets more choppy, which, in turn, means the ferry won't be quite as fast, i.e. you'll arrive at your destination a little later than planned. Don't worry too much about this, as delays are inherent in sea transport. It's the way it is. The good news is that this ferry is fully air-conditioned and offers in-cabin movies.
For your information, the Bintan to Anambas ferry departs Bintan every Monday, Wednesday and Friday. The return trip is every Tuesday, Thursday and Saturday. Note that there's no crossing on Sunday.
The cost of a one-way ticket from Bintan to Anambas is US$ 45. Advance booking is recommended, as there's only a single crossing to and fro every other day.
Incidentally, if you prefer to depart to Anambas from the Indonesian island of Batam instead of Bintan, then click Batam to Anambas ferry for these ferry details.
NOTE: If your time is limited and you just want to get to the Anambas Islands as soon as possible, then nothing beats the plane.