How do each of you handle the almost inevitable circumstance where a character trained in some of these skills becomes far more experienced and knowledgeable about that skill than the player will ever be?
Or, whenever the character is far wiser and more intelligent than the player? And in some cases, wiser and more intelligent than the player AND the DM combined?
It doesn't really change anything about the basic procedure of the DM clearly describing the situation, the player stating an approach, and the DM deciding if this calls for a roll, or not. Nor does it change anything about the outcome of said roll; the DM still presents a situation to the players where they must decide on a course of action.
The knowledge of the character, is merely taken into account by the DM when describing the outcome of an investigation of a trap, or when describing the outcome of disarming the trap. For example, a character highly skilled in disabling traps, may be able to deduce how a complicated trap works, which the DM then relays to the player, so they can state an informed approach to the problem. If the character is unskilled however, then this also affects how much information I relay to the player. As in my earlier example, the player may hear a buzzing coming from inside the trapped chest, but not know what is causing it.
Characters being more knowledgeable than their players is something that often occurs in my campaign. I see it as an excellent opportunity to educate my players on either the lore of the world, or on historical facts. I basically tell them things like:
"Your character knows that this statue represents the goddess of the sun, as is evident by the way in which the figure is depicted, and what she is holding in her hands." -And often this is preceded by a knowledge check.
Or:
"Your character knows that setting fire to the spiderwebs will not do much good, since spiderwebs, contrary to popular belief, are not flammable."
And often my players simply ask:
"Would my character know anything about this?"
In which case I'm always eager to provide them with extra information on specific subjects.