if you don't know the password, then you aren't the admin and have no business monitoring who is using the server. If you find a way to do so, then the admin isn't doing their job of properly securing the server.

Depends on what you're trying to do. Are you trying to find out who accesses a particular server (web, samba, nfs?) if you have access to the server.

If you have access to the server (as a regular user)

To see all IPs that are connected to the server and type

netstat -an

If you want to see access to certain applications (like web server) you're going to have to look through the logs, but you'll need the admins permission to do that.