The official rules, why the no-touching one exists, and what to do when it gets broken.

I train the scout elves before they go out, so the rules are genuinely my department. Families often treat them as arbitrary, and they are not. Each one exists for a reason.
Here they are, with the reasoning, and a proper fix for the moment every family dreads.
The famous one. Scout elf magic is carried on the surface, and human hands disturb it, which is why an elf that has been handled sometimes cannot fly back that night.
The practical reason it exists is just as important: an elf that gets carried around stops being a visitor and becomes a toy. The whole tradition depends on the elf being slightly outside the child's control.
Scout elves do not speak while they are in a house. They watch, and they report.
This one saves parents enormously, because a talking elf is a commitment to voicing a character every day for a month. Silence is a feature.
Elves move when everyone is asleep, which is why they are somewhere new each morning and never seen travelling. It also very conveniently means no child expects an elf to move while they are watching.
Every scout elf flies back with Santa. This is worth stating early, because a departure that has been expected for weeks is much easier than one that arrives without warning.
A gentler rule that I like a great deal. It is framed as protecting the magic, and what it actually does is stop one child spoiling it for a classroom.
It will happen. A toddler will grab it, or a child will pick it up to show a visitor, and then be genuinely distraught.
Do not panic and do not scold. The fix is well established up here.
This turns an accident into a three-day story with a happy ending, and children who have been through it usually treat the elf more carefully afterwards than those who never made a mistake.
Some families add house rules and they work well, provided they are stated at the beginning rather than invented mid-December.
That last one matters more than people think. An elf framed only as surveillance makes anxious children miserable. An elf that notices kindness is a much better houseguest.
Rules land differently coming from Santa than from a parent. Families who have him mention the elf by name, and remind children about the no-touching rule himself, find the whole thing runs more smoothly.
Have Santa set the rules himself.
Five rules, one emergency fix involving cinnamon, and one addition worth making: the elf notices good things too.
Get that last part right and you will have a child who looks forward to the morning rather than dreading the report.