I second @ff524's comment about the "key questions". Not all of them are equally applicable to each person, so decide what fits your situation the best.
Plan ahead, and try to memorize a few questions you want to ask.
Here are a few tips:
- Talk to the grads in that research group.
- Talk to the faculty leading that research group.
- Talk to the postdocs in that research group.
- Talk to other faculty in that department (but in other research groups).
- Try to observe interactions between grads and their advisors, if possible.
What you want to elucidate is the following:
- What are the expectations in terms of balancing fun/health/classes/research? Does your potential advisor appreciate friends/family, or is he/she more work-oriented?
- What's the expectation in terms of hours/week worked? Does that seem reasonable compared to other research groups?
- Do people in the group seem to get along with each other? (If not, that's a sign that there could be drama.) Do you think you could get along with the people there?
- Are people -- especially grads -- competing with each other for funding? This can put a strain on interpersonal relationships, unfortunately.
- Are people -- especially the faculty and/or senior grads or postdocs -- looking out for their own interests or for those of others (particularly yours)? In other words, will they be on your side and look out for you?
- Are people only interested in their own work, or do they show an interest in your abilities? Do they show an interest in you as a person -- beyond your academic capabilities?
- Does your potential advisor seem to appreciate his/her students?
If you're feeling really gutsy, you could ask a few more direct questions, but be careful.