If you have received any message on the notification bar regarding the new version upgrade, click on 'Yes, I am in' to proceed further.
For those who haven't received over-the-air (ota) upgrade notification, you may check for update manually by going to Settings --> About Phone --> System updates. And then you can proceed.
Before proceeding with the update, be sure to backup all your important stuff to your SD card though the upgrade didn't seem to harm anything, but it is better to be safethan sorry! I used Super Backup for that purpose, you may use an app of your choice.
Upgrading your Moto E should be a 4 step process -