Decorations do not perform any function other than to beautify your island!
You can get them in several ways:
✅ Completing quests
✅ As part of rewards (for example, for completing an Event Island)
✅ Finding them on Archipelago Islands (you can keep them in the Shop, then place them later on Home Island)
✅ Getting them from the Shop. Note that some decorations are free, but their number can be limited.
Decorations can be placed on Home Island in any free space and can be moved if needed. Decorate your island exactly how you want!
For more info on placing objects on Home Island check out the article Moving Objects Between Home Island and the Shop in the Gameplay section.