If you need to swap the columns in a table in Microsoft Word document, select a column and drag it to a new position. Select the left-most column (black arrow, left-click select vertically above the column) and then drag it (white arrow) to its new position.
Depending on the content of your table you may need to resize your table – AutoFit » AutoFit to Contents should do nicely.
The trick is in the selection techniques!