As you clear scenes you’ll gather fragments of paintings. Scenes marked with green puzzle piece icons have painting fragments.
Periodically tap on the paintings icon (the statue-like symbol in the Lobby) and you can scroll through which paintings are available and which fragments are remaining.
When you’ve found all painting fragments you’ll receive a special screen to direct you to Collections to assemble the pieces. A notification badge will also appear on the paintings icon in the lobby.
The Paintings menu will prompt you to assemble the painting fragments you've collected. Tap 'Assemble' (it costs coins to do so) and your painting will be displayed in full glory. From that point forward you can ‘show’ that painting if/when you desire.
Have fun and try to reach the goal of becoming a Top Collector!