In theory, to merge two tables in Word, you simply drag the lower table to line up with the upper table:

• Click inside a table cell.
• Drag the “+” table-handle and drag the upper-left corner of the lower table to be just a hair below the lower-left corner of the upper table, and Word will just merge them.

Sometimes it doesn’t work:

• Ensure that the second table doesn’t have a row marked as a heading.
• Ensure that neither table is wrapped (Set Wrapping to None on the Table tab of Table Properties).

Sometimes you still can’t drag them together. Select the lower table, and use Alt-Shift-UpArrow to move it, instead of the mouse.