AutoText entries are saved with the template - usually normal.dot unless you
specified a different template when you create the entries. Use Organiser to
copy the AutoText entries to a temporary template. Move the template to the
other computer and then use Organiser to copy them to your new normal.dot.

AutoText is stored in templates, in normal.dot by default. You do _not_ want
to simply copy normal.dot (with that name) to the new computer. Instead,
create a separate global template and use the Organizer to copy your
AutoText from your old normal.dot to that template. Then install that
template on your new computer (in addition to the normal.dot for that
system).

See http://addbalance.com/word/movetotemplate.htm for step-by-step
instructions on moving / sharing / copying / backing-up customizations
including AutoText, AutoCorrect, keyboard assignments, toolbars, macros,
etc.