Ozbert,
There are two ways you can do this.
Probably the best way is for you to enable Media Server on your copy of Media Center. You can do this from the Tools menu. You can also set options like having Media server start every time Windows starts etc.
Then everyone else, opens their copy of Media Center and goes to the File menu and select Library. They can try to search for running Media Servers (i.e. your machine) if this is found, they'll be able to see your library and play music without you having to share folders etc. If Media Center can't find your server automatically, they can manually set it up by adding your machine address from the Library Manager dialog in the following format:
m01p://yourmachinename
This is really the best way because even though they can connect, they won't be able to accidentally erase files etc.
Otherwise, if you want to do the things the file sharing way, you need to right-click on the folder where you are storing music and select "sharing..." and set up a share for that folder. The only catch is that other users will have to connect to that share by mapping a drive with the same drive letter that you are using (i.e. e:) so if they already have a drive e:, this won't work.
The first way is really better.
Let us know how you make out.
Jonathan