For those with the OTA ZIP file, ADB sideloading is the preferred method:

Google maintains a repository of factory images for developers.

Connect your handset to your computer via USB, launch the respective software, and look for an option to update or repair the system firmware. Unofficial Downloads and Custom ROMs

If your device gets stuck on the loading animation after updating, boot into your device's stock recovery mode and perform a Wipe Data/Factory Reset .

If you are still waiting for the OTA notification, you can manually install the update file using a computer. This method is for officially supported devices and preserves your data. You will need a computer with ADB and Fastboot installed.

Developers often port newer operating systems to older hardware. For Android 5.1.1, is the most popular choice. To find these downloads: Visit trusted development forums such as XDA Developers . Search for your specific device model's dedicated forum.