There are many approaches to decision-making - none of which is perfect. The three most basic forms of decision-making are autocratic, collaborative, and democratic.
Autocratic decision-making is defined by the leader making a decision with no input from the team followed by telling the team his or her decision. Collaborative decision-making involves a partnership or a collaboration between the leader and the team. In collaboration, there has to be in initial decision to receive genuine input. Democratic decision-making involves the leader allowing the team to make the decision irrespective of what he or she think. A leader cam employee all thee decision-making formats - or others.
Research has shown the best approach is collaborative with much lighter use of both autocratic or democratic approaches. Before a leader first meets with the team, he or she prepares to discuss personal approaches to decision making. This might involve stating one of the three frameworks discussed above. This lets the team know what to expect and avoid surprises.
No matter which framework you choose for a given decision, remember that all great decisions should be followed by great explanations. The team deserves honest and specific clarification for the decisions made. Not everyone will like all decisions but good explanations make the decision more just and acceptable. Explanations make a leader more fair and transparent.
Sometimes a leader makes decisions that he or she knows others will not like. For example, you might have to tell someone that the team will not get the budget increase they expected (or that there will be no raises). Perhaps someone didn't receive the promotion that they desired.
In addition to a quality explanation, a leader has to clearly own the decision. You should not blame someone else or a process. Do not suggest that some other person or committee made the decision. If difficult feedback is given to a team member with respect and ownership, they in turn will still respect the leader.
Decision making starts with understanding your style, explaining it to the team, using good explanations, and owning your decisions.