The most important step in debugging problems with the website (WordPess powered or any other) is to be able to get errors logged on the server side. This is not always as straightforward process as you might think and there are different approaches to have and find error logs.
It is very important to have server that is properly configured to log all errors. If your server is not set to log PHP errors (or other errors), you will not be able to get the error logs. Make sure you check and enable error logging on your server. This depends on your server type, and you need to consult with your hosting administrator or support team to enable this. PHP can be set to save errors in a single file or to save errors in multiple error logs based on the location where the error happens. If your server is set to save errors where they have happened, you will have error_log (or some other name, based on the PHP.ini settings) files all over your website folders, and you need to use FTP or some server based file manager to get these error logs. If your server uses centralized approach, all errors will be logged in a single file.
Getting centralized error log depends on your server type, control panel software used. Most common control panels for Linux based servers are cPanel and Plesk. Based on the software version (and even skin used from software front end), options to get error logs for these can be different. Make sure you contact your server administrator or support to learn about the error log on your server.
WordPress also provides method to keep own error log, and for that, check out this article.