How can I make toy cleanup easy enough for young children to do themselves?

You have to teach them and work with them until they get it. Once they understand they have to clean up their own messes they will become neater and organized. A good idea is to ask them to put their things away before they go onto another big toy project or go to another room.

Make the system easy for the people who actually use it: visible categories, reachable storage and a clear place for each item to return. For younger children, a picture label can work better than a written one.

My final check is practical: can you find what you need quickly, put it back just as easily, and see when the space is getting full? If not, simplify the categories or move the storage closer to where you use it. An organizing system should make life easier, not become another chore.