In a busy way — doing something with a lot of activity, and usually with your hands or body moving. If someone is busily writing, they are writing fast and giving it their full attention; if bees are busily working, they are moving all the time. The word almost always comes with a verb that shows action: busily typing, busily cleaning, busily taking notes. Two things worth knowing. First, 'busily' is not the same as 'busy' in the sense of 'I have no free time.' You would not say 'I am busily' to mean your week is full. It describes the LOOK of the action while it happens. Second, it often carries a small feeling from the writer, and the feeling can go two ways. Sometimes it is warm — the person is hard-working and it is nice to watch. Sometimes it is gently funny — the person is moving a lot, looking very serious, and the writer is hinting that all this movement may not be worth much ('the officials busily rearranged the chairs'). Which one it is comes from the sentence around it, not from the word itself. It is a slightly literary word; in everyday speech people are more likely to say 'hard at work' or just 'busy'.