You just need to install the Notezilla sticky notes app from Google Playstore and use it.
Yes. The cloud sync is available for trial. From Notezilla (on Windows), you can right click on Notezilla icon and choose Sync option to create a free trial Notezilla.Net account. You can use this to sync your notes with the Android app to test it. Once you are happy, you can purchase the Notezilla cloud subscription.
Watch this short video that perfectly depicts this feature:
You don't have to activate the license on android phone, because you already installed the app. Once you activate the subscription, the phone app with automatically detect and continue to sync every minute.
When you purchase the cloud version, you will get an email with instructions to activate the app on PC and also to activate the subscription.
To download Notezilla : http://www.conceptworld.com/Notezilla/Download