In versions v1.00 to v1.07, the characters are stored in the Windows folder. They're hidden files, so you'll need to go to View -> Folder Options -> View -> and click to enable the seeing of Hidden Files.
Next, look for files (approx. 66kb in size) named something like "dlinfo_#.drv" (The # is a number 0-9. Each save file has a different #.)
When restoring these characters, put them back in the Windows folder. Also make sure that your computer ID is the same as the one the characters came from.
In more recent versions of Diablo (v1.08, v1.09), the save files are located in the Diablo folder as "multi_#.sv" (The # means the same thing here as before.).
When restoring these characters, install Diablo and then patch it to whatever patch the characters are from. (i.e. If these are v1.09 chars, patch Diablo to v1.09 before proceeding.) Now you can copy the *.sv files back into the Diablo folder.
If you were talking about Single Player characters, those are named "single_#.sv" are are located in the Diablo folder.