When should a judge intervene in a match?
The Magic: the Gathering Tournament Rules (MTR) makes it clear that a judge should not intervene before a rule has been broken, but should intervene after a rule has been broken. In other words, a judge should be reactive, not proactive.


  Judges do not intervene in a game to prevent illegal actions, but do intervene as soon as a rule has been broken or to prevent a situation from escalating.


The Infraction Procedure Guide (IPG) states basically the same thing. Keep in mind that, as made clear by a recent rules update, the IPG is only meant to be used at Competitive and Professional REL.


  A judge shouldn’t intervene in a game unless he or she believes a rules violation has occurred, a player with a concern or question requests assistance, or the judge wishes to prevent a situation from escalating. Judges don’t stop play errors from occurring, but instead deal with errors that have occurred, penalize those who violate rules or policy, and promote fair play and sporting conduct by example and diplomacy. Judges may intervene to prevent or preempt errors occurring outside of a game


Judging at Regular (JAR) covers Regular REL. At Regular, the judge is allowed (but not required) to intervene for missed triggers. Again, this is optional, and you should intervene at your discretion.


  You should intervene if you see something illegal happen in a match, but beyond this you can exercise your discretion. For example, whether you step in when you see a player miss a trigger should be determined by the tone you want to strike for your event – it may be appropriate to provide this extra help in a more causal environment, but less so if your play group is more competitive.