Have you updated the base (free) MyBookTable plugin to the newest version? You can find it here: https://wordpress.org/plugins/mybooktable/
Making sure this base plugin is updated is the first step to ensuring compatibility with your upgrade.
The new upgrade should be uploaded to your plugins in just the same way you would upload any other plugin. Just go in your site dashboard to Plugins > Add New > Upload Plugin. Then, upload the ZIP folder you received when you purchased the MyBookTable upgrade.
Once the plugin folder is uploaded and installed, go in your dashboard sidebar to MyBookTable> Settings> Setup. There should be a field for you to input the API key for the MyBookTable upgrade.
Please let us know if you run into any other problems with MyBookTable, and we will be happy to help.