What permissions do I need do I need to grant a user for them to edit content in XPM? The user in question has a disabled "Finish Editing" button.
I think for editing components in XPM you need Component Management right on the website publication security, then Write permissions on the folders where the components of the page are stored. For applying changes on pages such as insert/remove content, switch Page Template etc... you need Page Management right on the website publication security as well as Write permissions on the Structure Group security where the pages are stored.
What rights/permissions did you assign so far to the Group that the user is a part of? Does the user see a Lock icon on the Page border and/or on Component Presentations borders?