How to formulate a computational problem rigorously?
a good resource on/for this, fairly well known by academics but not so widely known outside of specialists, is Mathematical Writing by  Donald E. Knuth, Tracy L. Larrabee, and Paul M. Roberts. there is a published book, lecture videos, and a set of notes. it is more written from the perspective of people attempting to master mathematical writing eg for creating papers, but all the advice is highly applicable to the case of laymen attempting to formulate problems precisely. mathematical writing while formidable to learn is the scientific approach to rigorously define/formulate—and as the book details, solve, eg via algorithms or proofs—computational/algorithmic problems.


Mathematical Writing book info
Mathematical writing lecture videos index
Mathematical writing CS1193 class notes


also, the classic Garey &amp; Johnson text, Computers &amp; Intractability does not exactly describe how to formulate problems precisely, but it does give many examples, and diverse theoretical/conceptual/technical "patterns", organized into sections of similar problems, which can be used as "building blocks" to describe computational/algorithmic problems.