What if someone arbitrarily edit the map?

I try to find the answer but with no luck.
I want to know whether OpenStreetMap verify edits or not?
It will be bad if some random people showing up, registering to edit the map and making some arbitrary edits.

OpenStreetMap is all its contributors. Vandalism does get detected, and reverted, as a result of people recognizing when something is going wrong in their area.

It happens all the day: https://nrenner.github.io/achavi/?changeset=52169856
We can just hope that another mapper finds this edits by qa tools or whodidit or osmcha.

There is also a new review feature in iD since a few weeks.

As pointed out by other posts, vandalism can and does occur and OSM relies on other mappers to detect and fix it.

In my case there are several areas that I am very interested in (around where I live, where relatives live, where I work, etc.). Using WhoDidIt with bounding boxes for those area I have created RSS feeds for those areas. I monitor the RSS feeds at least daily and each and every change that takes place I look at and decide if I agree with it or not.

99% of the time the changes are good and the mapper who made them will never know that someone else examined their efforts for quality. The other 1% of the changes I deal with, either by directly fixing them or contacting the mapper to learn what they were trying to do and then helping them do it better.

Is there a tutorial that explains to newbies how to 1) watch a list of areas, ie. be warned when someone edits them, and 2) if it is indeed vadalism, revert the changes ?

Although not difficult, reversion is probably not something that should be taught to newbies, as it can, itself, be abused. Generally it should only be used with the consent of the party who made the change, or by someone with the experience to know when there is no other alternative.

Wiki can give answers:

If it doesn’t help new mappers can search on https://help.openstreetmap.org.