Managing Permissions on a SharePoint Document Library (Asset Owners)
SharePoint has areas where files can be stored. These are called Document Libraries.
For example, this is a Document Library:

If you are the asset owner for one of these Document Libraries, you will have 'Full Control' of the Library. This means that in addition to being able to add and edit content in the Library, you can also manage the permissions that other people have in the Document Library.
There is more than way to change these permissions. This article will show you one way.
1. Go into the Document Library by clicking on it.
2. Go to the top-right corner and click on the 'cog' icon:

3. Choose 'Library settings'. Here you can change the name of the Library, but for now we will click 'More library settings'.

4. Here you will find a range of settings and information for your Document Library. The most important one for this purpose is the 'Permissions for this document library' option. Click on this.

5. This page will display a list of people who have access, and show you which access level they have. You can manage the permissions by using these options at the top of the page:

Let's break down what these options allow you to do:
(i) Delete unique permissions. This shows you that the Library has its own permissions, managed on this page. The alternative is that it inherits permissions from whatever level is above it, in this case the whole Site Permissions.
(ii) Grant Permissions. This will allow you to grant permissions to a user.
(iii) Edit user permissions. To use this, first select an existing user on the page. This will let you alter the permission level they have.
(iv) Remove user permissions. Removes all the user's permissions from this Document Library.
(v) Check permissions. Put in a user's name and check what access they currently have to this Library - including access via sharing links that have been sent to them.
6. Click on 'Grant Permissions'. You will see this box. Click 'Show Options'.

7. You will see this box:

(i) To grant permissions, enter the person's name or email address in the top box. You can enter multiple people.
(ii) Choose to send or not send an email to the person notifying them of the change by ticking the box. ("Email invitation").
(iii) The permission level is selected in the drop down box.

We recommend only giving out 'Read' and 'Edit' to normal users.
Read -- allows them to see all documents, but not edit.
Edit -- allows them to edit the documents.
Full Control -- allows them to do the above, and also edit people's permissions. (Don't do this unless they're an Asset Owner).