How to delete a File in Google Drive?

How do I write a Google Apps Script that deletes files?

This finds files:

var ExistingFiles = DocsList.find(fileName);

But DocsList.deleteFile does not exist to delete a file.

Is there a way to move those files to another Folder or to Trash?

The other workaround I would consider is to be able to override an existing file with the same name.

Currently when I want to create a file with a name already used in MyDrive then it creates a second file with the same name. I would like to keep 1 file (the new one is kept and the old one is lost).