Warning, this will replace your existing includes/skinMenuPart.php file. If you have changed this file, you will need to integrate your changes afterwards.
Make a backup copy of your web servers folder where you installed phpPeanuts into. Extract the examples archive you downloaded. If this results in a 'phpPeanuts ... examples' folder, move its contents, including the folders and their subfolders, into the same folder on your web server as you installed phpPeanuts in. Some of the folders will have the same names as some of the existing folders in your phpPeanuts install. The contents of those folders will have to be added to the corresponding folders on your web server. There should be no collisions except for the includes/skinMenuPart.php file mentioned above.
When you again run the 'index.php' script in the 'emptyapp' folder you should see the new examples menu. The examples will not work instantly because you do not have the right tables and data in you database. To make an example work, see the instructions in the tutorial on the phpPeanuts website.
Do not install the examples on your website. The examples are meant for testing and development only. There is no reason to expose them to the public. So keep them safely in the controlled development environment so that you can experiment with them without putting your website, existing application or other hosting accounts at risk.