The filesystem permissions are
only relevant to the webserver and the system you run the wiki on. The websever needs write permissions for all files and directories inside <dokuwiki>/data in order to make it possible for DokuWiki to read/write pages. Say your webserver runs under the system group www-data and you allow everybody in this group to read/write pages/directories in <dokuwiki>/data, you first have to change ownership of these files/directories (see man chown):
eg:
chown -R yourusername:www-data <dokuwiki>/data/*
Then you have to change the file permissions of the directories inside data/ so that the webserver is able to write files:
- to give write access to directories (read execute) for the owner (probably you) the first octal bit is 7
- to give write access to directories (read execute) for the group the second octal bit is 7
- to allow everybody else to just read the directory contents the third one is 5
Files only have to be read/write (not executable), thus, it's enough to set them to 664.
This has
nothing to do with the user/groups rights of the registered users of your wiki later. These are controlled via ACL (Access Control Lists), read the 3rd link I posted in my previous reply.
Keep in mind that the above is an example. Your webserver maybe runs under a different user/group like httpd for example so the chown command wouldn't work for you.
Of course you could just allow everbody to write files and set directories to 777 and files to 666 but that is not really save.
HTH