have you setup your router for internet connection?
for me I configure it using PPPoE for ADSL connection. I use a linksys router but all router should have almost same configuration.....it all depend on your ISP provider on how the connection setting go.....

you can set it up either use DHCP or static IP......
if for DHCP, setup your NIC using VASM for DHCP connection or try this
Stop any dhcp daemons that are running: as root, dhcpcd -k eth0
Restart the dhcp daemon for your device: as root, dhcpcd eth0
for static IP, use VASM to set static IP as root (same IP range with your router).......if your router is 192.168.1.1 then just set your VL to 192.168.1.2, subnetmask is same with your router setting
key in the gateway IP same as your router IP.........then try to ping 192.168.1.1 to make sure you and your router is network connected....
all is assume your NIC is working fine in VL......
to double check VL is detecting your NIC..........do below as root in VL
ifconfig -> if NIC is detected there should have some entry like ethx
lspci -> check whether VL can detect all the hardware in your PC/laptop
lsmod - to check what modules (equal to drivers for windows) loaded in VL/Linux
if you are not sure just post all the output to us....
if you are not sure what I am talking about and are new to Linux/VL and you are more familiar to windows based OS, find any Windows OS and plug in the router (after you do what ADSL configuration on that router). Use DHCP/Static to detect the router...
at the end, I am assume you are using ADSL connection...right?