Let's say you've removed a file from a page by deleting the link, or by replacing that link with a newly uploaded file. However, people are still finding the old file by way of outdated links or via Google. How do you remove this old file so people can't find it any more?
The short answer is this: the same way you uploaded the file.
Table of Contents
Delete files via the File Manager (IMCE)
My screenshots below are from a Drupal 8 site-- specifically, Anthropology's Drupal 8 site. Your site may look a little different, but the instructions are the same.
1) Create a Basic Page.
2) Click the Link icon, then click the blue Upload a File text.
3) This brings you to the File Uploader/Manager, where you can add and remove files.
4) Click on it to select it, then click the "Delete" option at the top of the file manager.
Drupal 8 Only: Figuring out where files are used on the site
1) Under "Content," click on the tab called "Files"
It's all the way to the right. If you don't see it, you are either on a Drupal 7 site, or you don't have sufficient permissions. In the latter case, you can talk to the person from your department who is in charge of the website and ask for their help.
2) Search for a file using part of the title
3) Click on the file to view it, or mouse over it to see its location in the file structure
So going back to my first set of instructions, if this was the file I wanted to remove, I would go into the File Manager, look in the Inline Files folder, and remove that. (Except that the File manager probably wouldn't let me remove the file because it is being used in two places. So I would have to go into those pages and remove those links from them first.)