A triggered ability is an ability that’s caused by a specified game action. They’re usually written in the
form "When [something happens] -> [effect]." The effect happens just after the specified game action is
taken. For example, many characters have triggered abilities that start with "When you flip to this
mode." The effects of these abilities happen immediately after you flip the character to the appropriate
mode.
What happens if more than one triggered ability triggers at the same time?
[Source: WotC]
Triggered abilities always happen one at a time. If all the triggered abilities belong to one player, that
player chooses their order. If both players have triggered abilities that would happen at the same time,
first the player whose turn it is handles all their triggered abilities in any order, then the other player
does the same with their triggered abilities.
Simultaneous triggers are resolved in the order you choose, but when do you choose the order? Is it when they trigger, or as each resolves? Example: Abilities A, B, and C all trigger simultaneously. Can I resolve A, see the results of that, and then choose whether I want to do B or C next?
[Source: WotC]
Yes. You choose which to use one at a time.
How do nested triggers resolve? Example: I trigger A, B, and C. B triggers D and E. What order do those resolve in? (Assuming choices, of course).
[Source: WotC]
Assuming you chose B as the first one, you can then choose A, C, D, or E.
Note that Wizards of the Coast changed this with the
Expanded Rules 2.0. When a nested trigger occurs, you put any unresolved triggers aside, resolve the new ones, and then go back to the triggers you put aside. So in the example above, it would be, assuming B first: B, then D/E, then A/C.