Situation 1: Entries saved to Google account
If you saved your entries to your Google account, normally all entries are synchronzied with Google server. Suppose all of your devices with the same account registered will be synchronized in a short time. You don't have to do further configurations.
You are suggest to check if all of your entries are synchronized. To do so, please visit web edition of Google Calendar and check if all entries are in place.
If all entries are in sync, just install New Calendar app, and configure calendar sync settings on your new device.
If some of your entries are not in sync, please follow the method below to manually backup and restore your calendar entries.
Situation 2: Entries saved to Local Calendar
Old device:
Download Calendar Backup: Import / Export app from Google Play Store , and export your calendar to ICS file (aka iCal file).
Tranfer the exported xml file to your new devices. You can email the exported file to your own mailbox, and check your email with your new device.
New device:
Download the same Calendar Backup: Import / Export app, and import ICS file that you exported from your old device in step 1.
Install "New Calendar" app from Google Play Store.
Configure calendar sync settings.
Old device:
Open New Calendar app > Menu > Data migration (widget) > Export. All widget's data will be stored in your SD card.
New device:
Install "New Calendar" app from Google Play Store.
Insert your SD card to your new device.
Open New Calendar app > Menu > Data migration (widget) > import.
Add a Todo list / sticky note on your main screen. Tap it to enter "Edit Mode".
Menu > Recycle bin > select your record that you want to recovery