Here are the steps to install the Democracy plugin:

1. Download the newest version from Wordpress.
2. Move the Democracy subfolder into your Wordpress’s wp-content/plugins folder (not the extracted folder but the folder inside it).
3. Activate the plugin and setup new polls. 

To insert a poll into a post.  Write {democracy: POLL_ID} on your post.  Replace POLL_ID with the id number of your poll.

Getting the widget plugin to work drove me bonkers.   In the Democracy zip package, there is a widget_democracy.php.  Put this file into the plugins folder.  Activate the plugin, then drop the new widget into your sidebar and BAM!… It works!… Maybe. For me, it worked, but the polls didn’t display correctly with my theme.

Here’s how it looked on my sidebar.

I got the widget to work with my theme by modifying the Democracy plugin code.  If you have encountered this problem, download my modified version and reinstall the plugin.

Here is how it looked with the modified version:

Another great poll that I’ve found is WP-Poll by Lester Chan, but unfortunately for me, I can’t get it to work.  Maybe other people will have better luck with it.