Run the following query:

SELECT s.username, s.program, s.logon_time
FROM v$session s, v$process p, sys.v_$sess_io si
WHERE s.paddr = p.addr(+)
AND si.sid(+) = s.sid
AND s.type = 'USER';

You can use the lsof (LiSt Open Files) utility to view information about which processes own file handles on a system. Since sockets map to file descriptors, lsof will show you which processes own socket connections. If you see that your machine is connected to another on TCP port 6234 (source or dest) and you want to find out which process(es) are responsible for the connection, run:

# lsof -ni tcp:6234

Note that when run as an unprivileged user, lsof will only show you file descriptors that you have permission to see. You must run lsof as root to see everything in the kernel.

If you want to use tcpdump to watch initiating connections (that is, the syn flag only is set indicating we're looking at the first third of the three-way handshake) on ports 80 and 443 you could do something like this:

# tcpdump '(tcp[13] & 0x3f = 2) and (dst port 80 or dst port 443)'