Typically, I locate Notepad and right-click, Run as administrator when dealing with any of the files within the %SYSTEMDIR%\System32\Drivers\Etc folder but you are probably already aware of that.
When saving your Hosts file from Notepad you need to change the Save as type: to All files (*.*) or Notepad will always try to tack on a .TXT extension.
If you want to try to rename from an elevated command prompt, click Start or tap the Windows key and type cmd then hit Ctrl+Shift+Enter all together. Acknowledge the UAC warning and provide credentials if asked. With the elevated command prompt window open you can issue the following command,
copy C:\Windows\System32\Drivers\Etc\Hosts.txt Hosts
That should make a copy of your Hosts file without the .TXT extension. You can keep the one with the .TXT extension as a backup or delete it.