The quick and dirty way to do it is to create a file named .maintenance at the root of the site– same directory as license.txt— and add a bit of PHP:
<?php
die();
Of course, you can create whatever markup and messages you’d like before the die();, but there is very little WordPress available since it fires very early in the wp-settings.php file.
If you want to see how to add and remove the file automatically, look at how the core does it.