I was looking for an answer to a save problem in the original game - the one just called "Zork" and included in the Zork Anthology bundle sold by GOG. It seems to me that Rokedo's query may be about this game (or perhaps one of the other DOS games) rather than one of the later ones.
I'm sure that s/he has found an answer or given up by now, but in case anyone else is trying to figure it out, I thought I'd explain what I finally worked out and tested.
It's a bit long, but i tried to be clear:
HOW TO SAVE A FILE IN ZORK I
The GOG version of the game has a facility when you set it up to create a new default location (as opposed to putting it on the "C:\Program Files (x86)\GOG.com\Zork Anthology". I keep my games on my E: drive, unless they are really big ones which need fast access to work. Even then, if possible, I keep my saved games (and I save a lot) on some other drive so as not to use up space on my precious SDD.
So, we will suppose that I save Zork files on "E:\Zork and Zork 1 on "e:\Zork\Zork1". This the GOG installer (for Win 7) notes as the default location.
When you want to save a file under Zork 1, you have to type "SAVE" at the command line, then press return. Then the program says, "Insert save disk then enter file name". This is a hangover from its DOS origins when many PCs only had floppy disks. The program does, however, helpfully tell you where it will look:
"(Default is C:Save\zork1.dat)" Note that reads C:Save and NOT C:\Save - the omission of the \ is not accidental - it says that the program starts in the current folder on the C: drive, then look for a sub-folder called "Save" and then saves your game to a file called "Zork1.dat" in that folder.
If you leave all the settings at default then you will find that you have one saved file called "Zork1.dat" in the "Save" folder under "C:\Program Files (x86)\GOG.com\Zork Anthology".
If you have changed your default folder (as I did) then you will need to enter "SAVE" (as before) and then when it asks for the file name enter Save and then the file name e.g. "Save\Zork1.dat" That, using my e: drive settings, saves the file to "e:\Zork\Zork1\Save" folder. The Save folder is created automatically by the installation program provided by GOG, wherever you choose to install it.
You may see that I have listed the file name as Zork1.dat - this is because you do not have to use Zork1.dat as your saved game name. I've been using Zork1.dat here since that's what the program says, but you can use a different filename and as many filenames as you choose - David1.dat to David99.dat or even a different extension name david07.zrk. These days we have enough space for many saved games at 13K each! I'd still recommend sticking to the 8.3 filename structure since this program runs in a dos box, however.
Just remember, leave out the "save\" bit and your file will go in the default game folder (which you chose during the installation procedure), add it in and the file will go into the sub-folder named "save" which GOG created at installation.