[Ultimate] How do you gant another LAN user permissions?

I've upgraded my home network file server to Windows 7 from XP.
The server houses all the media and photo files.
When it ran on XP, I had no trouble adding/deleting files on the serer from another computer on the same network.
But with the upgrade, I can read but cannot write or delete files on the server from another computer.
I've tried the file Properties - Security tab, but there seems to be no way to add a user from another computer.
Hours of search on the internet hasn't helped either.

Can someone enlighten me?