Note: The Dokuwiki to be upgraded is in /var/www/wiki on the machine called mybox, 
      I am logged in as root,
      and Dokuwiki version 2005-07-01 has been extracted to ~/dokuwiki/wiki/

From the directory above the directory that the old version is in (in this case /var/www):

Create a temp directory

mybox:/var/www# mkdir newwiki

Change into it

mybox:/var/www# cd newwiki

Copy the new version to the temp directory

mybox:/var/www/newwiki# cp -R ~/dokuwiki/wiki/* .

Copy the configuration customisations to the new location

mybox:/var/www/newwiki# cp ../wiki/conf/local.php conf/

Copy the changes.log file to the new location

mybox:/var/www/newwiki# cp ../wiki/changes.log data/

Copy standard data to the new location

mybox:/var/www/newwiki# cp -R ../wiki/data/* data/pages/

Copy media to the new location

mybox:/var/www/newwiki# cp -R ../wiki/media/* data/media/

Copy attic data to the new location

mybox:/var/www/newwiki# cp -R ../wiki/attic/* data/attic/

Presumably all namespaces now reside under the data directory (I don't use them so I am not sure), so copy all namespaces to the data directory as well. Change the ownership of the data directory (my Apache runs as www-data)

mybox:/var/www/newwiki# chown -R www-data data/

If ACLs were being used on the older version, copy them over:

mybox:/var/www/newwiki# cp ../wiki/conf/acl.auth conf/

Version 2005-07-13 seems to look for acl.auth.php instead of acl.auth

mybox:/var/www/newwiki# cd conf; ln -s acl.auth acl.auth.php; cd -

Tidy up: (keep a backup just in case, remember to delete it once you are happy!)

mybox:/var/www/newwiki# cd ..
mybox:/var/www# mv wiki oldwiki
mybox:/var/www# mv newwiki wiki

Test it.