First, ensure that you have installed the latest UT3 patch. At the time of writing the latest patch is 2.0. Nightblade will not run without the 2.0 patch.
For Windows Vista users: To install Nightblade, extract the zip file to your \Documents\My Games\Unreal Tournament 3\ directory. Make sure the file path structure is extracted.
For Windows XP users: To install Nightblade, extract the zip file to your \My Documents\My Games\Unreal Tournament 3\ directory. Make sure the file path structure is extracted.