How should a supervisor deal with a PhD student who behaves badly If a PhD student who behaves badly, e.g  being rude to other PhD students/staffs, distracting people in the same office by talking loudly or making noise..., should his/her supervisor do anything to deal with that student? If the answer is yes, what should a supervisor do?
There's obviously no universally accepted policy here (e.g., there are labs where brashness unfortunately starts with the principal investigators). You also need to be careful about what is meant and perceived as rude, as it is, partly, an artifact of culture (e.g. I've witnessed Japanese managers fake sleeping during business meetings, which I would be inclined to perceive as negligent or rude, but apparently expresses ritualized trust in their underlings acting for them). That said, and assuming there is confirmed rudeness, here is how I would handle this.

There should be a zero tolerance policy for rudeness towards staff as it is likely abuse of power, or perceived status. If you experience such rudeness towards other students during meetings, etc., I'd call the offender out as it happens ("There's no need for (X). We are all working together/(Y) didn't mean to imply this."); if during inter-student conversations you happen to witness, I'd first confirm with the person on the receiving end if they share your perception ("Is everything all right? You feel comfortable in our lab? (...)"), if the case is not blatantly obvious. In all cases that warrant action, I'd call the offending student for a personal meeting, in which you could outline that you prefer a more mellow lab, with suggestions how to better handle what happened. If this is a meeting with a repeat offender, be more forceful and tell them that they continue to be out of line, and that this has to stop. 

If you are personally disturbed by the noise level, you should say so - it's your lab. However, if you'd rather provide a quieter lab for your students, this is a common workplace problem with few known satisfying solutions. Here is an old question discussing the issue. The main problem is that some people prefer to talk while at work, others prefer to focus; if you take one side, you are likely to annoy the other. I find loud talkers rude and inconsiderate, but have never managed to change my surroundings in a lasting way.