Creative ideas are a central part of design thinking, whether solving engineering problems, generating interesting art, as well as developing successful products and innovations. Idea generation methods are a well-researched topic, and there is significant research that focuses on specific idea generation methods and how they perform. Furthermore, several method classifications have been suggested to help understand the cognitive mechanisms involved in creative ideation as well as differences between methods. Yet, the discourse is usually on which ideation method outperforms another or how to improve an ideation method rather than the elements, rules, constraints, and activities that comprise ideation methods. In this study, 88 well-documented idea generation methods are reviewed and analyzed. We find all analyzed methods consist of 25 basic mechanisms. The mechanisms are discussed and classified into idea promoting and implementation mechanisms. We suggest that rather than focusing research only on methods, there should be a parallel track of research on these mechanisms and their interactions to help increase our understanding of creativity methods, add understanding for practitioners on how to get the best advantages out of creativity methods, and finally improve the way that practical creativity is approached in education.