Word does not try to guess what information (fields) to insert from your
data source. It just presents you with a table, usually with one cell for
each label. (In some layouts there are what I call "label cells" and "spacer
cells" which just provide horizontal and vertical spacing. It's usually
pretty obvious which cells are intended to correspond to the labels).

At this point precisely what to do depends on which version of Word you are
using. If it is Word 2007, pretty much everything is on the "Mailings" tab.
If it is Word 2002/2003, I suggest you use e.g. View|Toolbars to enable the
MailMerge toolbar, then
a. in your first label cell, insert the fields you need from the data
source. Use the 6th button on the toolbar, just before "Insert Word Field".
(You can try using the ADDRESSBLOCK field but be sure that it inserts what
you want for all your data, as it suffers from a number of problems)
b. Format the fields as necessary (be careful not to modify the table
layout)
c. Use the Propagate labels toolbar button (I think it's the 11th button)
to copy your fields and layout to all the other cells, and to insert the
<<Next record>> field that tells Word to move to the next record for each
table cell. (Note1, yoiu do not need a <<Next record>> field in the first
table cell. Note2. On some tablet PCs and possibly some Windows Vista
systems the propagate label function does not work, in which case you can
try the macros at http://tips.pjmsn.me.uk/t0005.htm
d. Preview the merge using the toolbar and redo steps (a)-(c) as necessary/
e. "Complete the merge", either by merging to a printer, or merging to a
new document then printing it. The necessary buttons are on the MailMerge
toolbar.