Datasheets are dense, and the parts that bite you are rarely on page one. Here is the order to read them in.
Absolute maximum ≠ recommended operating
The single most misread table. Absolute maximum ratings are the values beyond which the part may be permanently damaged — they are not operating conditions, and nothing is guaranteed at them. What you design to is the recommended operating conditions table. Running continuously at an absolute max is a design error, not a clever margin.
Typ, min and max
Design to min/max, never to typ. "Typical" is the centre of a distribution at 25 °C with nothing else going on; it carries no guarantee. If a parameter only has a typ value, the manufacturer is telling you it is not tested — treat it as informative, not contractual. Note the test conditions beside every number (voltage, temperature, load): change them and the number changes.
A regulator's datasheet says "Absolute maximum input: 40 V". Your supply is 36 V. Is that fine?
Absolute maximum is the point beyond which the part may be damaged. It carries no promise that the part works there, and specifically no promise about accuracy, dropout or lifetime. The number you design to is the recommended operating conditions table, which is always narrower and is usually on a different page. Running continuously at absolute maximum is the classic way to build something that passes every test and then fails in the field a year later, because the derating curves — which nobody read — took the real limit well below the headline number long before you got there.
Try it — the derating curve behind the headline number
The curves say more than the tables
Derating curves, safe-operating-area (SOA), efficiency vs load, and gain vs frequency tell you how the part behaves at your operating point rather than at the one convenient point in the table. A regulator rated "1 A" often means 1 A at 25 °C on a 4-layer board with a specified copper pour — the curve tells you what you actually get.
Read the footnotes and the package
The small print carries the traps: "guaranteed by design", minimum load requirements, required output capacitor ESR range, start-up sequencing. Then check the thermal data (θJA is board-dependent and often optimistic — see heat sink), the package land pattern, and the part's lifecycle status before you design it in.