Inanimate objects can have spirits or energies attached to them, but they cannot become possessed. From my understanding, only living breathing creatures (humans most generally) can become possessed.
The most common type of magic that I know of (and have used) when working with poppets is something known as absent healing. You create the poppet and make it as close to the likeness of the individual as possible. You then fill it with items or pictures of the ill individual and healing herbs. After which, you raise energy and direct it toward the poppet. You visualize the poppet and the energy directed toward it healing or providing comfort to the individual that the ritual is directed toward.
If you can find it, The Witch Book: The Encyclopedia of Witchcraft, Wicca, and Neo-Paganism - Written by Raymond Buckland has information on both poppets and absent healing.
Interesting, I've always associated poppits with curses and binding (handy little guys to vent frustration on, maybe toss a little to the original), but I've never heard of their use in healing.
From what I've read in the book previously mentioned, they can be used for various magical workings though the most common forms are hexes and healing. I agree, they are quite useful tools. I've not done a lot of work with them (a few healing rituals here and there for friends and relatives), but that which I have done received great results.
Poppets can also be used in love spells. You can create a poppet to represent the target (person you want to be with) you could also create a poppet to represent yourself and use it to attract someone. You could also make a poppet to represent something in your life you wanted to remove for example an addiction.
Poppets can be made from different materials for example wax that's been melted and had herbs/ a photograph/ a name etc added to it. They are extremely versatile objects to work with.
Spirits can become attached to certain object or locations that held some sort of special significance to them in life. For example, many spirits refuse to leave a house because in life it was a place that brought them memories of great happiness. In the same manner, spirits can be attached to or attracted to houses that have a build up of energy. That being said, I've never heard of anyone actually attaching a spirit to an object. You might be able to create a servitor and use it to add to the power of the poppet, however.
Why exactly would you want to attach a spirit to something in the first place, if you don't mind me asking?
