How to (smartly) leave a postdoc early? I've already spent some months in a multi-year post-doc in Europe, doing clinical research. However, neither the project nor the life outside the lab seem good enough for my interests, and I'm planning on moving forward. 

I'd like go for either an industry job (1st choice) or another postdoc (2nd option). I have a few questions about this: 


Should I immediately tell my supervisor, or might I just give her
a short notice? 
Regarding the next move (either industry or other postdoc): will
it be hard to get a new position if I don't manage to get a
recommendation letter from my current supervisor? I guess I may have
to ask for recommendation letters to my PhD references. If this
could be a problem, how to avoid/minimize it? 
...And any general advice/experience about the topic would
likewise be appreciated.


Thanks,
If you have a good relationship with your advisor, consider informing him or her early in a very respectful way. He or she will appreciate you took the time. Why give them a reason to (potentially) write a less than stellar letter?

If you do NOT get a letter from your current advisor and go for another post doc, yes it will absolutely raise a flag. You could expect the topic to come up, or the interviewer make even contact your advisor directly.  However, if it really only has been a few months, simply stating the environment/locale/work/etc wasn't matched may be sufficient.