Decision making is a complex task that involves a multitude of perspectives, constraints, and variables. Multiple Criteria Decision Analysis (MCDA) is a process that has been used for several decades to support decision making. It includes a series of steps that systematically help Decision Maker(s) (DM(s)) and stakeholders in structuring a decision making problem, identifying their preferences, and building a decision recommendation consistent with those preferences. Over the last decades, many studies have demonstrated the conduct of the MCDA process and how to select an MCDA method. Until now, there has not been a review of these studies, nor a proposal of a unified and comprehensive high-level representation of the MCDA process characteristics (i.e., features), which is the goal of this paper. We introduce a review of the research that defines how to conduct the MCDA process, compares MCDA methods, and presents Decision Support Systems (DSSs) to recommend a relevant MCDA method or a subset of methods. We then synthesize this research into a taxonomy of characteristics of the MCDA process, grouped into three main phases, (i) problem formulation, (ii) construction of the decision recommendation, and (iii) qualitative features and technical support. Each of these phases includes a subset of the 10 characteristics that helps the analyst implementing the MCDA process, while also being aware of the implication of these choices at each step. By showing how decision making can be split into manageable and justifiable steps, we reduce the risk of overwhelming the analyst, as well as the DMs/stakeholders during the MCDA process. A questioning strategy is also proposed to demonstrate how to apply the taxonomy to map MCDA methods and select the most relevant one(s) using real case studies. Additionally, we show how the DSSs for MCDA method recommendation can be grouped into three main clusters. This proposal can enhance a traceable and categorizable development of such systems.