There are a few things you can do:
- Use the Debug Bar plugin http://wordpress.org/extend/plugins/debug-bar/
- Set WP_DEBUG to true in your wp-config.php file if you are looking for problems in a theme or plugin
- I created a plugin that allows you to dump any variable into the Debug Bar plugin: http://wordpress.org/extend/plugins/kint-debugger/ You should look at the global $wp_query var to see the query that is being executed.
Beyond that, there are dozens of debug plugins on the plugin repo.