Using tcpdump
To view incoming and outgoing packets on port 80
tcpdump -i eth0 tcp port 80
To view outbound traffic over port 80
tcpdump -i eth1 tcp dst port 80 and src host 192.168.0.10
To suppress verbose output, you just want to view source/destination
tcpdump -q -i eth1 tcp dst port 80 and src host 192.168.0.10
Nice -q option.