How do I remove (demolish) my own building or a placed item?
Building pieces (foundations, walls, floors, stairs, roofs and other pieces from the build menu): enter Build mode or take the mallet, look at the piece and tap Demolish.
On PvP servers you can demolish a piece only during the first 10 minutes after placing it — the timer is shown on the Demolish button. After that you will see "Unable to demolish: Demolition time is up", and the piece can no longer be demolished. On PvE servers there is no time limit.
You need building rights: if the building has a Tool Cupboard, you must be authorized on it. Otherwise you will see "Unable to demolish: No permission".
Placed items (doors, boxes, furnaces, workbenches, turrets and so on): if the item has a Pick up option, look at it with the mallet and pick it up — it goes back to your inventory. Open the lock first ("Unable to pickup: The lock must be open") and empty boxes and turrets before picking them up.
Some placed items cannot be demolished or picked up — for example High Wooden and High Stone Walls and Gates. Choose their spot carefully.
Tip: try your layout in the Sandbox first — there you can demolish anything.