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1. Copy DIRECTORY OnThisDay to wp-content/plugins (NOT DIRECTORY on-this-day). You will have something like /wp-content/plugins/OnThisDay/OnThisDay.php.
2. Activate "On This Day" in plugins page.
3. Set Options, add "On this day" widget at sidebar, or add OTDList() to sidebar, or main post loop.

Please visit this plugin's website for more information.