The path to your network drive is \\files.kk.lan\staff\username (just replace the username with your user name.)
When you are inside the OUAS network, you are not prompted for a user name and password to map your network drive, as you have already been authenticated when you did sign in to your computer. From outside the OUAS network, when you are using a VPN connection, you are prompted for your user name and password: give your user name in this format: kk\username
The path to the old Unix server where your public_html directory resides on, is \\staff.oamk.fi\username
For the Unix server, you are prompted for your user name and the related password. Here, do not use prefixes for your user name, just give your plain user name.
For instructions, see the guideline made for OUAS students, just replace the paths with the ones above.