After purchasing or signing up for the free trial, you will have received an email with a download link.
Use the download link to get the plugin file and then install via your WordPress admin dashboard by going to Plugins>Add New>Upload Plugin
Activate the plugin, this should automatically deactivate the free version.
If you check your installed plugins you should now have
Display Eventbrite Events in WordPress (Pro) – Active
Display Eventbrite Events in WordPress – Inactive, which you can delete.
Once you have your plugin installed and activated the next step is to connect to Eventbrite