So to move columns or rows, click on the header(s) to select them, then hold down Alt and drag one of the cells in the region to the new location. To make a copy hold down Alt+Ctrl. To just obliterate the destination don't hold down any keys.

If you hold down the alt key and try to move the column/row/cell, it won't work. Its important to press the mouse button first and then press the alt key.