Upgrading MacBook air from 10.6.8 to Sierra
I'm assuming that you have a Late 2010 MBA or later because an MBA prior to then won't support Sierra.  You will need El Capitan, instead.

I wouldn't recommend upgrading - I personally prefer doing a clean install and migrating over my Apps and Data using the Migration Assistant.

You should be able to download the Sierra Installer via the App Store since it was available to Snow Leopard Users.

Following are the steps you need to take to upgrade your MBA to macOS Sierra


Update (if needed) your MBA to the latest Firmware via a standalone installer.  This will help with the Internet Recovery.
Create a USB Installer of macOS Sierra
Backup your installation to Time Machine
Boot from USB and do a clean installation
Use Migration Assistant to move over your apps and data.