The wording of an error is the most useful clue you have. Here is what each one actually means.
403 Forbidden
The server found it and refused. Usually file or folder permissions, or a folder with no index file. See Fixing file and folder permissions.
404 Not Found
The site is working; that address is not there. A broken link, a deleted page, or - in WordPress - permalink rules that need re-saving.
500 Internal Server Error
The site's own code failed. A plugin, a theme, a PHP incompatibility or a mistake in .htaccess. The error log will name the file and line. This is a site problem, not a server outage.
502 Bad Gateway / 504 Gateway Timeout
Something the server was waiting on did not answer in time. Often a slow query or an external service that is not responding.
503 Service Unavailable
Temporarily unable to serve. Overload, or maintenance mode - in WordPress, often a .maintenance file left behind by an interrupted update.
"Error establishing a database connection"
The site cannot reach its database. Wrong credentials in the configuration, or the database is unavailable. Common straight after a migration.
Certificate warnings
An HTTPS problem: expired, or not covering the exact name being visited. The site itself is usually fine.
A blank white page
A fatal PHP error with error display turned off. See Fixing the WordPress white screen.
When reporting one
Quote the error exactly and give the address. The precise wording is what makes it quick to diagnose.
