What defines whether or not an ability is optional or mandatory?

Ruling: Triggered abilities always go on the chain when their trigger condition is met. Whether the effect itself is optional or mandatory is determined by the word "may" - if "may" is present, the effect is optional; otherwise it is mandatory by default.

Sequence:

• When a trigger condition is met (often starts with "When" or "At"), the triggered ability must be put on the chain
• The controller of the last item in the chain gets priority first
• Upon resolution, if the effect contains "may", you can choose whether to perform the action; if not, the effect is mandatory

Nuances:

• You don't "activate" triggered abilities - triggered abilities are triggered, while activate abilities are activated
• The distinction between putting an ability on the chain (mandatory for triggered abilities) and resolving its effect (which may be optional with "may") is important