How do I delete an object?

On the left side of the editor there's a button that looks like a little red circle with a minus sign in it. The button is inside of a drop down list, the button is the "delete currently selected object" button, so basically if you have the Tile selected, and click the button, the tile will be deleted, if you have a field selected and click the button the field will be deleted and so on. The editor makes you confirm what you are doing when deleting a Tile, but does not when deleting parts or "objects" as you've referred to them so be mindful. :)

Select the object. On the toolbar, all the way on the right side is a red icon with a white minus sign. Click that to delete the object.