How can I show groups in membership report columns?
The current correct way to create a custom report is to use an extension, rather than the manual process linked to in the question.

Updated documentation for creating a report extension is found here:

https://docs.civicrm.org/dev/en/latest/extensions/civix/#generate-report

The link in Donald Lobo's answer is now broken, but an old version of the document is still available here:

https://wiki.civicrm.org/confluence/display/CRMDOC46/Create+a+Report-Template+Extension