What should be done before upgrading MySQL?

Question

I need to perform an upgrade of MySQL on my web server. There could be many users connected to the server at any time, performing queries or updates on the database, or uploading files to the server. Besides putting up an advanced notification that the system will undergo maintenance during a certain period of time, what should I do to avoid the scenario of stopping MySQL service or the server while some user operations are still being carried out, which may lead to a corruption of the file system or the database?