As with many of these posts so far, I was slightly involved in a twitter conversation last week that touched on a topic I've been meaning to write about. What makes for a good postdoc experience? Keep in mind that I completely understand that everyone is different, and so the following certainly doesn't apply universally. In the very least this should provide some insight into how I run my lab and what I expect from people within the lab (including PDs), so if you're considering working with me in the future take these words as a brief intro into my style.
1) Be able to say "No" to your PI
As a PI, it's very easy to come up with ideas when reading papers and seeing talks. There are all sorts of new projects in every direction and this can be kind of overwhelming. Keep in mind that the goal as a PD is to write grants, papers, and generally be productive by seeing experiments through tho the end. It is very easy for your PI to say "why don't you try this" or "maybe this is something we should think about" without having to actually do the experiments. One of the most important skills as a postdoc is to be able to say no to your PI. If you can't say this simple two letter word without anxiety, you will simply run out of time in the lab and be swamped. Extra bonus, this skill often comes in handy later after you've landed that tenure track job and you're asked to be on every committee possible.
2) Don't take everything your PI says as gospel
Your PI is a researcher just like you...the difference is that they're more experienced at the job. They've likely interpreted more data sets, read more papers, dealt with more rejection, etc... Simply stated, your PI has had more practice than you at your job. However, within this context, realize that PIs are wrong all the time. If we mention/cite a paper we may be misremembering it. There may be some new and better paper (which we haven't read because, trust me, it's hard to keep completely up on the literature in real time) that has disproved the first. There's a very real chance that the data we remember is more nuanced than we think it is. Always read the primary literature and interpret the data for yourself.
3) It's OK if your PI disagrees with you, but know when their evidence is overwhelmingly good
That being said, your PI isn't wrong all the time. There will be times when you want to argue over interpretation, and that's OK, but learn to know when you've lost the argument. Trust me, this will save you much time and effort in the end.
4) Help your PI be a better mentor
I am very good at being me as a researcher. I understand my own body rhythms and know when my most efficient working hours are. I know exactly what type of mentorship and interactions I needed to succeed. I understand myself reasonably well, but everyone is different. One of the most difficult parts of mentorship at any level is understanding what the other person needs from you in terms of opinions, information, and interaction. How do you motivate someone else? You will have a much more successful PD (I think) if you can discuss with your PI exactly what kinds of feedback and interaction you need and expect. Think about what kinds of feedback you require in order to succeed. Have an open discussion, in the end this is the best possible situation for both of you.
5) Don't be afraid to start small pilot side projects
Never be scared to start small projects on the side (for me small projects require less than about 100$ of new supplies). If money's an issue your PI will let you know. If you read about a new technique, try it and see what happens. Screen a bunch of isolates for presence of a PCR product. Mix two strains together to see who wins. This will give you added experience designing experiments and interpreting data in a new framework. In the very least you will learn the hugely important skill of cutting bait when things aren't working. In the best case scenario you will develop projects that you can take with you to your new lab.
6) Have continuing and open discussions with your PI about which projects you can take
Data sets change. Some experiments work and others don't. The most tension I've seen between PIs and their PD always seems to be over ownership of projects. Be clear with your PI about what you want to take with you even before you start applying for jobs. If you've had some small side projects work, tell your PI and have the discussion about who "owns" what. The more open you are the clearer limits will be when you are starting your own lab.
7) Don't be afraid to apply for independent fellowships
I've seen some cases where PIs don't want their PDs applying for fellowships because the time invested could be better spent on experiments, I strongly disagree. If you land a tenure track job, you will have to write grants for a living and the more practice the better. Even if you have a paycheck through your PI's grants, independently earned fellowships are a huge CV boost that can help you land a job. It's worth the effort, just make sure you don't drop the ball on your experiments.
8) You are not hired as a technician
You aren't there to have your PI feed you experiments to do, you're hired as a PD to be an independent thinker. To design new experiments, to read papers, to try and figure out new directions for the project to go. It's a bad situation if your PI is hawking over you and giving you precise direction at every step. You will not develop the skills needed as a tenure track researcher and your PI missed a golden opportunity to push their research program forward.
9) Take every opportunity to speak, teach, and mentor
It's very likely that you will have to do these things when you are a PI, and (as I've said a bunch of times above) the more practice you have the better. If you have the chance to give guest lectures or teach a course (so long as your PI is OK with this) go for it. You will never understand a topic better than when you have to explain it to someone from first principles. You may even see the problem in a new light or make new connections. Practice can only help you out later when your doing these things continuously.
10) Enjoy your life as a postdoc
Your postdoc is likely the last time, for a while, that you will get to decide where you want to live. The job of being a PD is about performing experiments and writing papers, but you are a person outside of the lab too. A researcher's life is stressful, so use the time outside the lab to enjoy the world around you. Feel free to go to a lab X to work on an awesome project, and completely disregard the outside world, but I'm just saying that there is more to life. I often find that some of my best thinking gets done while I'm out running...There might not be as awesome a project in lab Y, but if the quality of life is better you may end up with a more fruitful and fulfilling postdoc experience.