First of all install the Widgetkit component/plug-in for your new site.
If it is Joomla and you have some experience with phpMyAdmin (or a similar tool):
xyz_ being your old site’ table prefix and
abc_ that of your new site, you could then export all records from
xyz_widgetkit_widget and import them into
Should you be in WordPress: The Widgetkits are saved along with other content in the table
wp_xyz_posts. Look for
WIDGETKIT in the column
post_type. You could selectively export these records and import the lot into the corresponding table of your new site’s database.
Where in doubt about working in a database please ask your site’s webmaster for assistance.
Of course make sure the images are copied to the same relative location on the new server.