OSX equivalent to sudo chgrp -R www-data <directory>
On Ubuntu you use "www-data" because that is the user the Apache process runs as. You can identify the user Apache will use by checking the config file. On my Mac, it looks like this:
$ cat /etc/apache2/httpd.conf
[...]
User _www
Group _www
[...]
So one way to make your files writable would be to chgrp them to _www.