From Policy Concepts in 1000 Words: The Policy Cycle and its Stages:
The classic way to study policymaking is to break it down into stages. The stages have changed over the years, and vary by country, but the basic ideas remain the same:

Descriptive. Let’s simplify a complex world by identifying its key elements.
Prescriptive. Let’s work out how to make policy, to translate public demands into government action (or at least to carry out government policy).

[image of the policy cycle]
A cycle divides the policy process into a series of stages, from a notional starting point at which policymakers begin to think about a policy problem to a notional end point at which a policy has been implemented and policymakers think about how successful it has been before deciding what to do next. The image is of a continuous process rather than a single event. The evaluation stage of policy 1 represents the first stage of policy 2, as lessons learned in the past set the agenda for choices to be made in the future:

Agenda setting. Identifying problems that require government attention, deciding which issues deserve the most attention and defining the nature of the problem.
Policy formulation. Setting objectives, identifying the cost and estimating the effect of solutions, choosing from a list of solutions and selecting policy instruments.
Legitimation. Ensuring that the chosen policy instruments have support. It can involve one or a combination of: legislative approval, executive approval, seeking consent through consultation with interest groups, and referenda.
Implementation. Establishing or employing an organization to take responsibility for implementation, ensuring that the organization has the resources (such as staffing, money and legal authority) to do so, and making sure that policy decisions are carried out as planned.
Evaluation. Assessing the extent to which the policy was successful or the policy decision was the correct one; if it was implemented correctly and, if so, had the desired effect.
Policy maintenance, succession or termination. Considering if the policy should be continued, modified or discontinued.

The cycle is useful in many ways. It is simple and understandable. It can be applied to all political systems. The emphasis on cycles highlights fluid policymaking.  There is also a wide range of important studies (and key debates) based on the analysis of particular stages – such as the top-down versus bottom-up approaches to the study of policymaking.
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However, the stages approach is no longer central to policy studies, partly because it does not help explain what it describes, and partly because it oversimplifies a complex world (does it also seem to take the politics out of policymaking? In other words, note the often-fraught politics of seemingly-innocuous stages such as evaluation). The policymaking system may be seen more as a collection of thousands of policy cycles, which interact with each other to produce much less predictable outcomes.  Indeed, many of the theories or concepts outlined in this series serve as replacements for a focus on cycles (see the The Advocacy Coalition Framework and Multiple Streams Analysis).
The prescriptive side of cycles and stages is a bit more interesting,  ... [see the post for more]