Moving to a new device is pretty easy on Android. Make sure your 1SE account is backed up completely on your Google Drive account. This happens automatically and pretty quickly on wifi.
On your new device, go to the Play Store and download 1 Second Everyday again. Once installed and opened, 1SE will ask you to log in with your Google account. Make sure this is the same account you had on your previous phone. This is because your 1SE can't be transferred to a different account and is only backed up to one Google account.
Now after your login, 1SE will start the sync process. This could take some time depending on your wifi connection. So it's best to do this over night while plugged into a wall outlet.
TIP: It's always best to double check your Drive account and make sure there's available space on it so 1SE can work properly.