One of the ways that a team can set priorities at work is by coming together as a group and reaching a full pre-operational consensus and understanding of what the priorities actually are. This should be done first, even if doing so requires additional up-front time before going into operating mode, as advised by organizational psychology practitioner Eva Rykrsmith, writing for The Fast Track. Communication skills play an important role in making sure that all members of the team are on the same page and have internalized the priorities once they have been set up.
Project managers may often take on the task of deciding the team's priorities, but whether the priorities are developed jointly by the team or dictated by management, setting up a clearly defined ordered list for everyone to follow is necessary for the team to stay focused, as noted by former Microsoft project manager Scott Berkun in a book excerpt published by Microsoft Developer Network. An ordered list serves as both a guideline and a set of boundaries to keep team members from straying or becoming distracted by lesser priority tasks. A key attribute in project management is the ability to say "no" when a team member begins to turn their attention to a lesser priority task or activity that they would prefer to work on.
Debates regarding the ordering of priorities are acceptable, as long as they occur during the time devoted to up-front planning. Once those priorities have been placed into an ordered list, however, arguments or debates need to be cut short by bringing the team's attention back to the ordered list.