Hello,
usually you can take the DNS in your own network, like your router, or a
public DNS, like Google's 8.8.8.8. Public DNS has the disadvantage that
it can not resolve other devices in your private network. This is not an
disadvantage as long as you don't want to communicate with other
devicers in your own network.
You should check out if you have set up a correct IP / Gateway adress
and subnet mask as static for your home network on your Android device,
or if your DHCP server (usually your router) is setup correctly to hand
out IP adress, Gateway and subnet of your private network, and that you
have reserved enough pribate IP adresses for all your devices.
Stefan