If it's not your project, you may not want to update things yourself. Some modifications may have been made to the Spine runtime and you can end up removing them in an update.
But if it is your project, all you have to do is delete the files from the previous version, and and import the new version.
(1) If you know where all those folders are kept, just delete them.
(2) Download and import the unitypackage from this link: http://esotericsoftware.com/files/runtimes/unity/spine-unity.unitypackage
EDIT:
The unitypackage is updated now. You can now use that. Updated this post to reflect it.