The first stage in formulating a hypothesis is to develop a research idea. A hypothesis suggests a solution to a particular problem or set of problems, but some problems are more important or relevant than others. The steps involved in identifying a relevant and interesting research problem depend upon the particular field of study, but the general steps include observation and reading the relevant journals, articles and books by the leading scholars on the related topics. A third essential ingredient is imagination. The 19th century philosopher/scientist Charles Peirce referred to the imaginary function as "abduction." Peirce's idea of abduction was intended as a necessary complement to deduction and induction.
Sketch out a basic outline for the hypothesis. The initial outline can take the form of a general hypothesis that helps to narrow down the topic. The process of writing and thinking through the topic clarifies the issue or issues. The precise nature and extent of the problem may not be entirely clear at first or you may be trying to accomplish too much. In other words, you may be focusing on too many things. Narrowing down the topic makes it possible to zero in more clearly on the topic.
Formulate the hypothesis as an if-then statement. The first part of the hypothesis states the problem and the second part serves as an answer to the problem. This is a simple way of characterizing the issue, but it serves as a general framework with which to formulate a hypothesis. In order for a hypothesis to be persuasive and legitimate, it must be logically consistent and based on evidence and facts. Flawed or mistaken premises or facts will invalidate the hypothesis.
The final stage in formulating a hypothesis is to develop a way of proving that the hypothesis is true. At a basic level, this requires establishing some type of experiment to test the hypothesis. Testing the hypothesis depends upon the discipline or field of study. Hypotheses in the sciences depend upon empirical tests and observations, while those in mathematics depend upon logical inference and consistency. The humanities, art, literature and philosophy use a variety of methods including empirical observation and logical inference.