Using NetworkManager more or less implies that you have a take away and travel around computer (like a laptop) and thus connect to all sorts of networks. That would mean that you use DHCP and the different DHCPs will provide you with different, for that network applicable, DNS configurations, like it will give you different IP addresses, netmasks and default gateways.
When you, on the other hand, have a fixed place/network you connect to (like desktop and computer room systems), you will preferable use ifup and then either use DHCP, or configure yourself including DNS.
YaST can only be used to setup connections using ifup.
If you’re using NetworkManager, you have to change the settings in NetworkManager itself:
Click on its icon in the system tray and select “Manage Connections…” in the lower right (the connection settings are also reachable via “Configure Desktop”->“Network Settings”).
Select your connection and click “Edit…” to get to the DNS settings (amongst others of course).
Depending on your connection type, the icon may look different for you of course. But I hope you know which one it is.
If not, just look for “Network Settings” in “Configure Desktop”…