Instructions
Gather four apples from the orchard. This creates the apple essence you need to paint the podium.
Return to your workshop, and select the "Work on Task" option.
Choose the Mayor's picture from the task list, and select the "Podium" task. This takes you to the building screen.
Build the podium from the ground up using the wood pieces highlighted on the menu.
Select the "essence" option, which is located next to the "paint."
Select an apple from your inventory, and then touch a part of the podium to paint it with the apple essence. Repeat this process until the whole podium is painted with the four apples.
Click "Done" in the upper right corner, and the podium will appear in your inventory.
Return to the Mayor, speak to her and select the option that allows you to "Give" the item. This allows you to open your backpack, remove the podium and place it in the Mayor's office.