Download the plugin archive and expand it (you've likely already done this).
Upload the popularity-contest.php file to your wp-content/plugins directory.
Go to the Plugins page in your WordPress Administration area and click 'Activate' for Popularity Contest. This will create the database table used by Popularity Contest.
Congratulations, you've just installed Popularity Contest and it is now tracking data for you.
Optional: go into Settings > Popularity to modify the values of each view and feedback type.