know users who are logged in without logging in
 

How do I find out which users are currently logged in to a remote computer without myself logging in.
I dont know how can that be done using finger.
Suppose I try
$finger remote_machine
No such user
$If i try finger @remote_machine
cannot creater socket.

Did you try to finger username@remote_machine? (no pun intended)

If the service is running and accessible it will show you the info you need about that user. However, exposing the finger service to remote access over an insecure network is frowned up as it is inherently insecure so unless your on a secured LAN or VPN it is strongly recommended to disable/firewall the finger service.

On the other hand, you can schedule a cron job to priodically email you a list of currently logged on users ($users $w and $who all work).

Yes I did that and that to generated the same error cannot create socket

How about ssh user@host w? You're authenticating long enough to run the w command, but you're not really logging into an interactive session.

$finger @remote_machine
cannot create socket.

Usually means finger has been disabled. Is this on your own network?

Finger listens on port 76 [edit: I mean"79" of course], is this open?
Is the remote machine configured to respond?

This is my institute network and I dont know who to check whether the port for finger is open or not.
Isnt port for finger 79

So you can answer your own question in the future:
Check if it's open/listening using nc or nmap, if appropriate for your work situation. This is commonly disabled.