You can download a freeware Macintosh program called WhatRoute, which will allow you to do ping, tracroute, nslookup, and other assorted tasks. The guide posted above is still pretty relevent for the Mac, and also relevant for any type of broadband connection. A couple Mac-specific things, though...

The equivalent of winipcfg on the Mac is the TCP/IP control panel. This will list your IP, netmask, gateway, and default DNS server. If the IP claims to be something beginning with 169, chances are you have some problems. Don't bother trying to ping, it won't work. One solution to this is to close TCP/IP, open the System Folder, open the Preferences Folder, and trash the file "TCP/IP Preferences". Immediately reboot your Mac and reconfigure your settings, then quit and save. This works surprisingly often. While it doesn't seem to be an issue with newer versions of Open Transport, it would sometimes happen that when you crashed, your preferences file would be corrupted, leaving your Mac unable to obtain an IP address.

And if you're using the wrong kind of twisted cable between your computer and your DSL/cable modem, it will never have worked at all. That's something you'll probably have to fix.