1. Working towards a publication is essential for you (even if you don't achieve this goal!!!) - so find a mentor in the lab you are joining (may be the PI is approachable enough, or talk to a senior postdoc) and make this clear to them. Formulate this something like "working towards a publication will help me focus and be more productive, as well as give me a sense of accomplishment" - all of which are true, by the way. This will make you not sound like a mendacious creep who simply wants to show up for a couple of hours a day to buff up the resume.
2. Do you still have a choice of labs or are you set on where you are going? if it's the former, join the lab that does have a manageable project for you, as well as has a strong publishing record. Also you want a lab where you will have somebody willing to mentor you - show you the ropes and spend time teaching! But wherever you end up, be very proactive; ppl in labs are busy and unless they see that you are EAGER to learn and do the work, you will not get the help you need. Don't wait for them to offer.
3. At the end of your lab stint, make a presentation for the team - regardless of what your results are. The presentation may be about your project, about the enzyme/pathway they are studying, or even better about something new in the field that they will be interested to hear about.
4. By all means, shadow! and ask questions when appropriate! Trust me, requesting to shadow will make you look interested and proactive, and absolutely nobody expects you to know much. Best strategy would be to know what kinds of patients you will be seeing that day, and at least review that anatomical site. If you top it off with having read an article (Nature Reviews Onocology has great review articles, and NEJM has great "case presentations") will make you look like a star. Go to Google Scholar --> Advanced; there you can input your search words ("prostate cancer radiation oncology"), the journal, and the years of publication (focus on the last 5 years, as rad onc is a very fast developing field).
Best of luck