If you are running Windows 9x, click Start -> Run -> winipcfg.
Navigate through until you see your device which you go online with.
(If you use a modem to go online, then navigate to your modem, if you go online via LAN (Ethernet, Wireless etc) then select your appropriate adapter that you go online with.
Once you selected your adapter, look at your IP address. If your IP address is located in these ranges, then your are on LAN.
10.0.0.0 - 10.255.255.255
172.16.0.0 - 172.31.255.255
192.168.0.0 - 192.168.255.255
For Windows XP, click Start -> Run -> cmd -> OK -> ipconfig -> Enter.
We will see your adapter's IP address and just look at the IPs above to see if you are on LAN. (This should work with NT based systems too.)
To help you further more, please provide more information about your connection. What operating system you have and what connection you use to go online etc.