Welcome to LQ!!
Open a terminal, enter "su" to become root, and enter "ifconfig". You should see something like this:
eth0 Link encap:Ethernet HWaddr 00:04:5A:82:F4:A7
inet addr:192.168.1.46 Bcast:255.255.255.255 Mask:255.255.255.0
inet6 addr: fe80::204:5aff:fe82:f4a7/64 Scope:Link
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
<<deleted extra stuff>>
What we are looking for is the IP (inet addr) and the word "ON". If you get something like this, then try to ping the modem:
if that works, try:
If all this works, then you should be able to open a browser and start surfing. Otherwise, tell us what results you get at each step.