METHOD 1:
Open a terminal by pressing CTRL+ALT+T and type the following:

ifconfig

You get an output like this:

eth0      Link encap:Ethernet  HWaddr 78:84:3c:e7:0f:5a  

          UP BROADCAST MULTICAST  MTU:1500  Metric:1

          RX packets:0 errors:0 dropped:0 overruns:0 frame:0

          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0

          collisions:0 txqueuelen:1000 

          RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)



lo        Link encap:Local Loopback  

          inet addr:127.0.0.1  Mask:255.0.0.0

          inet6 addr: ::1/128 Scope:Host

          UP LOOPBACK RUNNING  MTU:65536  Metric:1

          RX packets:5666 errors:0 dropped:0 overruns:0 frame:0

          TX packets:5666 errors:0 dropped:0 overruns:0 carrier:0

          collisions:0 txqueuelen:0 

          RX bytes:1611838 (1.6 MB)  TX bytes:1611838 (1.6 MB)



mon0      Link encap:UNSPEC  HWaddr CC-AF-78-B3-E5-0F-3A-30-00-00-00-00-00-00-00-00  

          UP BROADCAST NOTRAILERS RUNNING PROMISC ALLMULTI  MTU:1500  Metric:1

          RX packets:877993 errors:0 dropped:115 overruns:0 frame:0

          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0

          collisions:0 txqueuelen:1000 

          RX bytes:533724526 (533.7 MB)  TX bytes:0 (0.0 B)



wlan0     Link encap:Ethernet  HWaddr cc:af:78:b3:e5:0f  

          inet addr:192.168.1.2  Bcast:192.168.1.255  Mask:255.255.255.0

          inet6 addr: fe80::ceaf:78ff:feb3:e50f/64 Scope:Link

          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1

          RX packets:377839 errors:0 dropped:0 overruns:0 frame:0

          TX packets:353884 errors:0 dropped:0 overruns:0 carrier:0

          collisions:0 txqueuelen:1000 

          RX bytes:460380208 (460.3 MB)  TX bytes:35093507 (35.0 MB)

As mine is wireless I can see my ip address in wlan0 . If your is a wired connection you can see it in eth0 or pppo if yours is a pppoe connection.

METHOD 2:
In the top panel of Unity go to the Network Icon (Network Manager) and select Connection Information.

You will see all the information including the IP (IPv4 and IPv6) of any device connected. In this case it is only showing one device since I have only one connected, but if I had multiple ones it would show each one on a different tab