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The only-slightly-more complicated method is to grab a d6 and assign different outcomes to its numbers. For example:

At this point, you may also want to decide/dice for how the trap would normally be disabled by someone with the key – that is, unless the chest owner designed the trap to trigger regardless of whether the actual key was used or not! Some dungeon-dwellers and mean like that.

Eventually you will have a custom-to-your-tastes-and-needs, finely-tuned trigger random table that you can use when stocking dungeons or when deciding hazards on-the-fly.

There's another method for deciding this that eschews dice entirely, which is to go by the player's behaviour: the trap triggers when the player commits to the risky behaviour. "I unlock the chest!" without checking for traps? Trap springs as soon as they roll to unlock. You can describe the actual timing of the trigger any way you like, since the player has locked-in their course.

The only-slightly-more complicated method is to grab a d6 and assign different outcomes to its numbers. For just one example based on my own trap tastes:

At this point, you may also want to decide/dice for how the trap would normally be disabled by someone with the key – that is, unless the chest owner designed the trap to trigger regardless of whether the actual key was used or not! Some dungeon-dwellers are mean like that.

Eventually you will have a custom-to-your-tastes-and-needs, finely-tuned trigger random table that you can use when stocking dungeons or when deciding hazards on the fly.

There's another method for deciding this on the fly that eschews dice entirely, which is to go by the player's behaviour: the trap triggers when the player commits to the risky behaviour. "I unlock the chest!" without checking for traps? Trap springs as soon as they roll to unlock. You can describe the actual timing of the trigger any way you like, since the player has locked-in their course.

Further to "it depends on the nature of the trap", you might find "Appendix A: Random Dungeon Generation", Table V.-I on page 171 of the Dungeon Master's Guide (1st edition) helpful as well. It's a table that you pick from or roll on to determine the nature and trigger for a trap.

It gives a variety of trap types, providing inspiration, and it demonstrates several ways in which a "locked chest" may be trapped in ways that may or may not be directly connected to the lock – just because a chest is both locked and trapped doesn't mean they have to be connected! In fact, the less predictable such a connection is in their experience, the more incentive your players will have to take nothing for granted about such dangerous objects as chests in dungeons.

There's another method for deciding this that eschews dice entirely, which is to go by the player's behaviour: the trap triggers when the player commits to the risky behaviour. "I unlock the chest!" without checking for traps? Trap springs as soon as they roll to unlock. You can describe the actual timing of the trigger any way you like, since the player has locked-in their course.

This method will appeal to some DMs and not others. If you choose this method, you might wish to add "Are you sure?" interrogatives as a regular part of your back-and-forth with your players, if you haven't already. Few things keep them on their toes more than the DM asking for confirmation of a risky choice, especially when there doesn't seem to be any unfortunate results when they go ahead anyway. Then, the times that they do suffer the consequences, it's clear that they walked into their fate willingly.