Assuming you're using Word XP or 2003, you may be able to see the old Word
2000 dialog using Tools|Customize|Comands, select category Mail Merge and
locate and drag the command "insert Merge Field" to a toolbar. (Sorry, I'm
not sitting at a machine with XP or 2003 on it right now, so can't be sure).

Otherwise, I generally just insert all the fields I need in one go, ensure I
can see the underlying field codes (use Alt-F9 to make them look like {
MAILMERGE myfield }), then cut/paste them where I want them. Irritating, but
marginally less annoying than having to go into that useless dialog box time
and again.

If you're setting up a lot of mailmerge documents and find yourself
inserting the same field names again and again, you could consider using
autotexts or creating a toolbar with buttons to insert the fields you
wanted.