My scenario:

I have a document type call CommonPage.

Implement the ContentService.Saving method in an Event handler called CommonPageEventHandler (ApplicationEventHandler).

I created a document type called News that inherits the Common Page.

Implement the ContentService.Saving method in an Event handler called NewsEventHandler (ApplicationEventHandler). It is a class library separate from the CommonPageEventHandler, then a separate dll.

How do I know which executes first?

The two have an implementation ContentService.Saving. But need the CommonPageEventHandler run first.

As the Umbraco understands which to run first? It is to say to the Umbraco which to run first?

These links do not say anything about the execution order when you have more than one EventHandler with implementation Content Events.

https://our.umbraco.org/documentation/getting-started/Code/Subscribing-To-Events/

https://our.umbraco.org/documentation/Reference/Events/Application-Startup