This question is a bit weird to ask because generally speaking, a normal answer will be "the same way you used to work as a PhD student" but I am not sure if I picked a "bad" habit from my previous experience.
As a first task as a postdoc, I have received a short abstract with an expected research outcome (a detailed technical report) and some sub steps to achieve the research outcome. These sub-steps are important tasks on their own and will need some research and time, I understand that. So, here is what I did, I read articles in the first week and I prepared a small draft (one page) highlighting key ideas that will help me achieve the first sub-task. The issue, is that I needed some further clarification about the abstract as this will help me decide which direction I should follow next, but at the same time, I wanted to send something to the PI in the first week and not "disappear" after receiving the research abstract, but I haven't received a response in 3 days and I don't know if I created a good impression.
Now I am wondering, how does a postdoc work in the first place (research methodology)? am I expected to have big results every-time I reach out to the PI? When I was a phd student, I used to send weekly (sometimes 2 weeks) updates to my supervisors. These updates were either progress status or problems I was stuck at! Is this approach acceptable for a postdoc?