I should make the following point very clear:
All major development or changes to a site should be performed on the development machine and thoroughly tested before being implemented or ported to the live site.
There will be times, however, when you simply have to make some changes directly to the live site even if it is only to implement upgrades that have already been tested out on the development server. If this is the case, then rather than allow users to browse a site under maintenance, visit the Maintenance mode page in the Development section, and select Put site into maintenance mode, provide a Maintenance mode message to display if the default one is not suitable, and get on with your work.
Be very careful when ...