1. First things first, you should run your Xbox 360.
2. Then you have to find Settings via the menu and choose Network Settings.
3. In the Available Networks screen, please select the type of your connection: Wired Network or Wireless Network.
4. After that, you should click Configure Network.
5. In the appeared window, select Basic Settings tab and choose DNS Settings.
6. To manually assign DNS servers to Xbox 360, you should choose Manual in the Edit DNS Settings window.
7. In the Primary DNS Server field, you should enter primary DNS server for Xbox 360 (126.96.36.199 - EU DNS or 188.8.131.52 - US DNS) > press Start > click Done.
In the Secondary DNS Server field, you should enter secondary DNS server for Xbox 360 (184.108.40.206 - EU DNS or 220.127.116.11 - US DNS) > press Start > click Done.
Note: You should use the closest server to your real location as Primary DNS server and the second closest server as the secondary ones for Xbox 360.
8. Restart your Xbox 360.