The Crane is a one-time use item that only works in the Capital City. First click the Crane, then click an object on the board whose location you don't like. That object will be removed from the board and put "into your hand." You can then put the object either in another location on the board or into your inventory for future use.
Obtaining a Crane
As of the time of the original post (2012-08-23), the Crane is only available via the in-game store. Below are the steps for buying it: