There are a number of factors that determine if a user can 'edit' a document (file, meeting, policy etc).
1. The 'owner' of a document can normally edit it - that is the person who created it
2. If a user has 'editor' permissions when they see the document - this can be as their profile has been set as an editor or the containing folder has them set as an editor
3. They are set as an 'additional author' (usually added by the owner to allow them to update it.
Anyone who has Editor permissions to a document can authorise additional people as Editor of a document (known as 'Additional Author'. Here are the steps to add an additional author.
Open the document, and click the Actions/Edit button, then click the 'Who can access this' button. The use the 'add Additional Authors'' section. Add the desired people to those who can edit the document. If you are happy with the change click the Submit button otherwise press Cancel.
Note: When the 'Additional Authors' option is used then this overrides the ability of users with Editor profiles to edit the document....all the people or groups you want to be able to edit the document need to be added as additional authors.
A user will know if they can edit a document by looking at the Actions Button. If it is there and Actions/Edit is available they can edit. If the Button is missing or does not have these options this is because they are there as a 'Reader' and not an Editor/Author of the document. If a user needs to edit a document where they are 'locked out' then please contact the document owner to adjust the settings on that document.