Yes you can! There are three types of decoration:
Core set - these decorations can be earned by completing sets of moths or missions, then used to adorn your sanctuary. Each decoration has at least two forms. The first is earned by completing a set; the second is earned by perfecting it.
Event set - there are 3 decorations in an event set. The first and second are earned like core sets and the 3rd decor is event exclusive and can only be obtained by perfecting the set before the event ends. These all have abilities.
Premium - these are purchased from the shop for glowbucks or real money. There are 7 of these all with an ability each.
Look out for holes in the branches around your environment. This is where you can place your decorations. Tap on a hole and you will be prompted to open the space using coins, then tap the “unlock” button that appears at the bottom of the screen. Tap the open spot again and then the “place” button.
A window will pop up showing the decorations you have available. To place one, tap it then tap the "place" button.
Finally, tap the back arrow button at the bottom of the screen to return to your forest.
If you'd like to swap out an existing decoration, the process is the same. The button will just say “swap” instead of “place”.
Please note if you have lots of decorations you will need to scroll up and down in the decor inventory to view them all!