Congratulations. General tips I find useful in starting any new jobs:
- Arrive on time and spend your time working and leave on time. This sounds basic but not everyone is doing this. If colleagues see you early at work, spending "most" of your time doing real work not hanging around or checking Facebook and leave on time, then it is a good start.
- Do not try to prove that you know everything. Ask questions. Try to have the right balance between independent working and being afraid of asking questions.
- Now for Postdocs. PI expect you to help PhD and Master student. They expect you to write papers even for experiments carried out by others. They expect you to take care of some administration stuff. Usually Postdoc is the right hand of a PI. I think the key point is to work independently but in a different way than a PhD student. A PhD student cares only about his research with little interest on what is going on in the institute/research group. A Postdoc involves in wide topics and in the group. A Postdoc could do a research in a different topic than his PhD research.
To conclude, work hard without killing yourself. Do not try to prove that you know everything. Expect a different and wider scope of work.