Dear PIs: How can a new hire politely probe you for details?
Just ask, actually. But a good way would be to ask for a list of publications of the group and a list of colleagues you would be working with. You could then introduce yourself to one or more of them and ask for information so that you don't need to ask too much of the PI. 

Some groups will have already made some or all of this available on a web site associated with the institution or the project. You could get started there if it exists. 

I'm assuming that you already have been offered a position, rather than just being in the application stage. 

You could even consider visiting the lab and meeting a few people if that is an option. Speaking with other postdocs might be especially valuable.