Proper approach to updating assets

Say my 3D artist sends me a file containing a bunch of 3D assets (environment and items) and I go ahead and position the environmental pieces, and also separate the items, duplicate them, place them around the scene, modify them, etc. If my artist makes a tiny little amendment to this file, how can I update it into the Unity project without losing all my modifications?

If by an asset you mean a mesh or a texture, those are stored as files on the file system beneath the Assets directory. If you physically replace those files with new versions supplied by your artist, Unity logical constructs such as GameObjects and Prefabs will use these new versions of the meshs and textures.