If you have a router with logging enabled, and if it has this logging feature, since many routers are different from one another, you can get to the router which is probably at 192.168.1.1 if your IP address of the computer is 192.168.1.x where x is any number from 0 to 255, but usually a number from 2 to 255. Most routers default to address of .1 so if you know your IP address of the computer is even 10.10.112.2, then type 10.10.112.1 in the browser and if the router is at that IP you should be greeted with a logon box for username and password. Most routers have a label on them that states the default user and password. Most people keep the same user name and just change the password, while some routers only allow for password change with user name not able to be changed.
Knowing this username and password, you can then browse in the router log if its enabled and look at where people have gone maybe.
The other method of getting info is to have a 2nd computer on this shared network and have wireshark running and monitoring all network traffic. You can get tons of info through wireshark, especially if passwords and user names are unencrypted as clear text. Some chat rooms use to show as clear text in which you could probe the network and watch what they are typing on the other computer to post to the chat room etc. BUT Wireshark takes some getting use to. Its a powerful tool if you know how to use it, but if your not an IT guru, it can be a pain to learn to use and decifer a block of information that looks like this below:
%$ * J A
C K &^%
WENT &^
T o &@*!
*&TH*E#
%#ST*&
ORE&^%
In which the message of "JACK WENT To THE STORE" can be found in clear text unencrypted within the captured ascii data.