You don't mention whether this is a "Web server" that you get to through HTTP
or a file server that you get to through a network file share or mapped drive.
In the first case you will need some server side script to write the file. In
the latter case you can run the file from the server and use the FileLocation
variable to specify where the file is going to go.
WriteExtFile(FileLocation^"UserData.txt", "The stuff I want to write")
This will put the file in the location of the file that you're running, up on
the server, so anyone who runs that file from the same location will write to
the same file. The published file should be able to do this just as if it were
running on your machine.
Now... you have to worry about possibly reading and writing to the same file
at the same time unless you break the info up in different files with the
user's name or id or something to keep track of them. This is a common approach
for really simple data store. Usually people use a subfolder and user ids.
WriteExtFile(FileLocation^"UserData\\Student"^User ID^".txt", "the data")
The next step is most often a small database app, MS Access is quite common
for local data storage.

HTH
Mike
====================
Mike Baker
Adobe Community Expert
mike-baker at cox dot net