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Here is the solution:
Go to settings => Enable Wi-Fi => Long Press on the required network => Click on Modify Network => Enable Show Advanced Options => Then change the DNS and then Save it.
I don't think this is possible (at least not without root).
Why do you want to change the DNS-servers?
If you own the wireless network you connect to, then you might be able to configure the DHCP server to send alternate DNS-servers to your xperia ray when it connects.
you can check out thses easy steps from waselpro vpn service
just like the op said long hold on the selected wifi =>modify network=>tick show advanced options=>change ip settings from DHCP to static=>change DNS1 to e.g 8.8.8.8 or 8.8.4.4
How did u solve it? i had the same problem with xperia zl
i got the same problem. I can't save it. -.-