I'm currently using my Shield to simply stream media (via apps like Kodi/Terrarium TV etc) over my WiFi. I never load media manually onto the Shield.
I've realized now that I really need a VPN. What exactly do I need to do to verify that my Shield utilizes my PIA VPN over the Wifi?
PIA has an app (i believe you have to use a mouse) for android. Use that.
I wonder if you have used PuppetMaster.TV which has a built in Teleportation feature but also let's you use your own VPN client? Use the REKODI repo for common plugins.
Astril vpn also has an android app you can side load
Best option is getting a ddwrt based router and policy based routing over the vpn... That way any host in your house can use the Internet.
But that's a bit more complicated
I side loaded PIA onto my shield tv. Once side loaded, it works quite well.
I have been using PIA side loaded on my Shield for 2 years now. No issues.
PIA worked, but was sideways on my Shield (rendered better on my nexus player for some reason). You can grab the apk from apkmirror.
You can also use "Open VPN for android" which has a decent android tv interface. Both are MUCH easier to navigate with a mouse.