Updating the snap package

I have such a question. I created a snap package published let’s say version 1.0. After I created the same package but already updated with version 1.1. The question is how the package is updated on the user’s side

On the user side, snapd periodically pokes the store asking for updates of the snaps installed in the system. Once you upload a new revision of a snap to the store and publish it to a channel, at some point when snapd asks again, the store will let it know that there is an update. Snapd then proceeds to download the new snap (or just the delta from the previous revision if available).

This is clear.
And how to properly publish a new version of the package and so that the changes that the user made were not changed

You’d probably want to consult the documentation which covers the process: https://snapcraft.io/docs/snapcraft-overview

This documentation describes the process of creating a snap package.
And I want to find out how to update my package to a new version

Edit snapcraft.yaml, build the new snap, upload it to the store, make a release to a desired channel.