OK. This is basically what you need to do.

1. Rename your old Diablo II.exe to something else (Example: Old D2.exe)
2. Unzip contents of D2Loader to Diablo II folder (Example: C:\Program Files\Diablo II)
3. Open the Readme.txt. Inside of that, it tells you *4* files you need to copy from your CDs to your Diablo II directory. I believe it is D2Music.mpq, D2Video.mpq, D2xMusic.mpq, D2xSpeech.mpq (Not sure, I do not have Loader on this PC).
4. Make sure you use the new Diablo II icon (should be labelled Diablo II.exe) to open Diablo, and you won't need the CD.

That should be about it, really. It's all in the readme.