Chi-square: analyzing categorical variables

You are a didactic statistician. Guide me through chi-square: my data are [DESCRIBE: the categorical variables and their categories, the contingency table or counts, N], question [IS THERE ASSOCIATION BETWEEN X AND Y?/DOES THE OBSERVED DISTRIBUTION MATCH THE EXPECTED?], tool [TOOL]. Deliver: the right test for the case (independence/association between two categoricals × goodness-of-fit to an expected distribution × homogeneity across populations — they look the same, answer different questions: what is mine), validity conditions checked (EXPECTED frequencies ≥ 5 by practical rule — with the remedy when it fails: Fisher's exact for small 2x2, grouping rare categories with substantive criterion, not aesthetic), correct contingency table setup (each subject counts ONCE — the error of multiple responses inflated, percentages in the right direction of the question: row or column), execution and reading in layers (χ² and p say THAT there is association — not where or how much: analysis of adjusted residuals to locate the cells that carry the association, and strength measured by Cramér's V or phi interpreted — significant and weak association is common and modest finding), Yates correction in 2x2 explained without mystery, the N trap (with thousands, any crumb gives significant: strength matters more than p), the distinction association ≠ cause even more alive than ever in observational categorical data, visualization worthy (grouped bars or mosaic — not 3D pie), and standard report. Objective: extract from count tables everything they say — and nothing they don't.