Sounds like you're looking for a sniffer type thing :
I've found IPTRAF to work well for giving an overview of what's coming in/out of your machine.
http://freshmeat.net/projects/iptraf/?topic_id=152
Ethereal is better at actually looking at the contents of packets.
http://freshmeat.net/projects/ethereal/?topic_id=152
To look at log files use vi.
*cough* Sarcasm there, but you might want to look through freshmeat (chop the urls above) and search for syslog. There are *TONS* of utilities for doing stuff to syslogs from simply viewing them, colourising them so they're all pretty, to sending them off to remote locations for security reasons.
Stuff internet related might be contained within :
/var/log/messages - lots of stuff
/var/log/secure - logons, and um.. 'secure' related stuff
/var/log/xferlog - what people have transferred using ftp
Slick.