How to re-post an old post?

You may use the Old Post Promoter plugin: http://wordpress.org/extend/plugins/old-post-promoter/

This plugin promotes old posts by sending them back onto the front page and into the RSS feed. It does it randomly choosing an eligible post and updating the publication timestamp. The post then appears to be the latest post on your WordPress blog. “You down with OPP? Yeah you know me!”