One of the best ways to see the harbour is to take to the water in a kayak. It's more personal than just sitting on a ferry, and you are able to visit places that the ferries do not go.
It is possible to hire a kayak and go for a paddle yourself, however on some parts of the central harbour you are required to have a licensed guide with you. It can also be quite dangerous kayaking on a busy harbour with many large and fast moving boats whizzing around, especially if you've not kayaked much before or are unfamiliar with the area.
A guide will also know the most interesting and picturesque places to visit, and most will be able to tell you about the history of the areas you paddle through.
There are a number of companies that operate kayak tours in Sydney. They include