The Core Mechanic

Roll an icosahedral die (d20), add some numbers, perhaps subtract some numbers, and compare to a target number. For the most part, you decide what to do, the DM makes sure it is neither trivial nor impossible, sets a target, and you roll a die. Then you determine the outcome. More complex situations (like combat) involve more rules, and every expression of the rules involves this flow: decide (talk out your plan), determine (roll dice and add up numbers), evaluate (discuss what happens).

Simple Rules, Many Exceptions

Because of the creative nature of a play experience, the rules can't cover every scenario, and even for the ones it does, many circumstances will feel exceptional. Most of the rules are a special treatment of some exceptional circumstance that arises from and extends the basic rules. Very little is ironclad, but that doesn't mean you always throw it out.

Specific Beats General

Like cascading style sheets, if a specific rule conflicts with a general one, the specific rule wins. Many of the powers and features in the rules are a specific exception to a general rule, that would simply not work at all unless you apply them this way.

Always Round Down

Baby, you're going to have to do math. Unless instructed otherwise, round down to the nearest whole number.