How do you put a playlist on wordpress blogs?

You can use HTML5 MP3 Player with Playlist or Audio Playlist Manager with Autoresume plugin.

You can find it here: Wordpress.org/extend/plugins/search.php?q=playlist">http://Wordpress.org/extend/plugins/search.php?q=playlist

Also, some useful plugins can be found here:

http://www.Wordpressfamily.com/category/plugins/