Download the plugin archive and expand it (you've likely already done this).
Put the 'anserlinks' folder into your wp-content/plugins/ directory. Afterward, you should have a folder structure like this: wp-content/plugins/answerlinks/(a bunch of files).
Go to the Plugins page in your WordPress Administration area and click 'Activate' for AnswerLinks.
If you are using a version of WP prior to 2.1, upload the included prototype.js to your wp-includes/js/ directory