Activated abilities are written in the form "Cost: Effect." Some keyword abilities, such as equip and crew, are activated abilities and will have colons in their reminder texts.

Triggered abilities use the word "when," "whenever," or "at." They're often written as "[Trigger condition], [effect]." Some keyword abilities, such as prowess and fabricate, are triggered abilities and will have "when," "whenever," or "at" in their reminder text.

If you counter a delayed triggered ability that triggers at the beginning of the "next" occurrence of a specified step or phase, that ability won't trigger again the following time that phase or step occurs.

An activated mana ability is one that adds mana to a player's mana pool as it resolves, doesn't have a target, and isn't a loyalty ability. A triggered mana ability is one that adds mana to a player's mana pool and triggers on an activated mana ability.

Abilities that create replacement effects, such as a permanent entering the battlefield tapped or with counters on it, can't be targeted. Abilities that apply "as [this creature] enters the battlefield" are also replacement effects and can't be targeted.

There are many important moments in the story, but the most crucial—called "story spotlights"—are shown on cards. You can read more about these events in the official Magic fiction at http://www.mtgstory.com.