• Set $wgCustomLogsLogs in localsettings as a list of log names/keys.
• For this example we'll say you want to create a log named "kittens"
• Create the page MediaWiki:Log-name-kittens with the name of the log, for example "Kitten Log"
• Create the page MediaWiki:Logentry-kittens-kittens with the display text for the log
  • You may specify parameters $1, $2, etc
  • $1 is User (with markup)
  • $2 is User
  • $3 is Page
  • $4 etc may be specified by you, the limit is given by $wgCustomLogsMaxCustomParams (default 3, so $4 through $6)

• This can be done via the api action customlogswrite
• Ability to write custom logs is governed by the right writecustomlogs, default available to anyone
• For different logs, parameters custom1, custom2, etc may have different meanings, but this numbering system was chosen to avoid retaining deprecated API parameters for logs that are no longer in use
• Can decide to publish the log in recent changes or not

Planned is eventually to have an interface similar to Tags where you can add and remove logs, and stop using MediaWiki namespace for things; this would also allow for a right for creating and removing logs separate from sysop. However the extension is functional as-is so that's not high priority currently.