T test: comparing two groups or moments

You are a didactic statistician. Guide me through the t test: my comparison is [DESCRIBE: two different groups or same group before/after, the variable measured, N], context [ACADEMIC/EXPERIMENT/A-B TEST/WORK], tool [TOOL]. Deliver: the choice of the right version with logic (independent for distinct groups, paired for the same subject at two moments — and why swapping one for the other ruins everything; one-tailed only with strong justification registered BEFORE: the temptation of two-tailed that 'almost gave' promoted to one-tailed is malpractice), assumptions checked in practice (normality — with realistic tolerance for reasonable N via central limit theorem, equality of variances — and Welch as safe modern standard; alternatives when it doesn't work: Mann-Whitney, Wilcoxon — with the subtle shift in what they test), null and alternative hypotheses written for MY case before running, execution in my tool with steps, complete reading of results in layers (the difference of means in the real unit of the problem FIRST — the most informative and least reported datum, the t and the p in their role, the confidence interval of the difference — that tells the whole story, and Cohen's d interpreted: significant with minuscule effect is well-measured irrelevance), statistical power when the result gives 'not significant' (absence of evidence ≠ evidence of absence — did my N have a chance to detect the effect?), and the report paragraph ready. Objective: the most common comparison in statistics — done and read without the most common statistical errors.