Assuming you already installed the game, go to Program Files and search for the OpenXcom folder. Next, unzip the nightly and drag n' drop its contents onto the OpenXcom folder, overwriting the previous files, like so:
@Orz: Although this will not do any damage, it is not necessary at all. The nightly download contains everything you need, except for original game files.
@davef:
Correct steps:
1. extract nightly to a new directory (anywhere... for example on your desktop)
2. go to sub-directory "UFO" (you can see it on the screenshot above)... it will be almost empty with only 1 file called "README.txt"
3. open "README.txt" and read, which files from the original game you need to copy into this sub-directory
4. copy the files
5. run the game using "openxcom.exe"