I'm aware of what's in the DMG.
I was asking about what you do, since you said you "require an appropriate check" which seemed to be in contrast to your summary of @Charlaquin's gameplay in which “In some cases you determine their actions will have no chance of failure”. The implication seemed to have been that you never determine actions to have no chance of failure and always test them with an “appropriate” check. I had assumed that by appropriate you had meant something like “using an ability and/or proficiency that corresponds to the fiction in some way”, but perhaps the concept of appropriateness being used also extends to checks only being suitable when nontrivial actions are declared, in which case my example would be a poor one. Notice, however, that in @Charlaquin’s method, a distinction between trivial and nontrivial actions is not needed. The DM simply decides whether the declared action could fail and if that failure would have meaningful consequences. Actions that might be deemed trivial probably wouldn’t meet those criteria, so no check would be called for.
To go back to @Charlaquin's example, an action was attempted "to try to disarm this trap by wedging something (I no longer remember what, maybe it was a dagger or something) through the seam to hold the lever in place while they opened the door, which I determined would succeed without need of a roll." Presumably, this was a nontrivial action insofar as disarming the alarm system was important for the party's plan to open the door without setting off the bell and as the prospect of inserting an object through the door-gap with sufficient force and positioning as to immobilize the lever doesn't sound (to me) like something that could be relied on to succeed on the first try. Multiple attempts may have had to have been made, and yet, the mechanism having already been noticed, and the possible existence of other factors such as an absence of time pressure (so no negative repercussions for repeated attempts), the DM decided to describe the success of this (nontrivial) action.
Now, you as DM might have called for a check in this situation, having a particular DC in mind for the disarming of the door alarm, but my question is do the players in your games ever have their characters attempt a nontrivial, non-mundane action in the fiction for which you don't feel a check is an appropriate way to resolve?
If I think there is a chance for failure or uncertainty, I ask for a check. Typically I'll ask for a specific skill (or the player asks to use it), although a player may have a reason to use a different skill or ability I hadn't thought of. If they find an alternate path to avoid the trap altogether then they don't care if the trap is disabled or not.
But descriptions of how, in @Charlaquin's example, they disable a trap will never be anything other than fluff and has no impact on the target DC because it's not the player physically disabling the trap, it's the PC.
The exception to the general rule is persuasion and intimidation, in almost all cases I need details on what they say. Along the same line if I know they can't fail the check even on a 1 I won't bother making them roll.
I thought I've been clear every time I ask this question.