Good catch on the installation documentation. It didn't get updated since all the work to support Twitter's new API change that requires all requests to be authenticated. There should have been an admin notice after you upgraded (or installed) that prompted you to go through the necessary steps, but I've updated the installation instructions as well. they now read:
1. Use automatic installer to install and active the plugin.
2. You should see a notice appear in your admin that links you to the settings page.
3. Follow the instructions to setup your Twitter app and authenticate your account (an unfortunate step made necessary by Twitter's API changes).
4. In WordPress admin go to 'Appearance' -> 'Widgets' and add "Twitter Widget Pro" to one of your widget-ready areas of your site
The automatic installer is when you choose "add new" from the plugins page and either search for the plugin or upload a .zip of it.
If you have problems with authentication, please open a support ticket at the URL Rootside gave you. The review isn't really a good place for support.