Just like all other people :)
In the camp, a safe and secluded place is chosen so that no one interferes with indulging in thought. If we stand on stones, then, as a rule, it is somewhere behind a large stone, which is convenient to approach. If in the snow, then sometimes the toilet is corny built from snow. Snow blocks are made with an avalanche shovel and a toilet is built from them. The architecture depends on the mood of the builder, the weather and other subjective circumstances. Sometimes there are real masterpieces made of snow. A place "beyond the bend" is looked for on the glacier if there are no options at all.
On the route - as needed. Depends on the site. On a difficult site, usually not before. On a simpler site, you ask the team not to look closely at you. Normal piping usually allows you to do this without removing the system. Down jumpsuits often have a zipper on the back, because at altitude in low temperatures it will not be very fun to be exposed.
In general, it happens that you find "traces of a person's presence" even on small rock shelves on the wall routes. If you put it on - what to do. I will not say for all climbers, but in my experience, when you go to the mountains with people, you are in difficult conditions and generally connected with them in the literal sense of the word, somehow everything becomes simpler, there are less conventions and constraints. Life is very easy to arrange for just a couple of days.
I am not a climber myself, but they told me.
On a glacier, if there are no trees or bushes and there is a limited space, then a stone is taken, "Toilet" is written on it, and people walk for it. And how they walk when climbing - I don't know, probably not in any way, only in parking lots.