In the top-right corner of the screen, there should be several icons, similar to Windows' system tray in the lower-right corner or Mac's comparable section also in the top-right corner. One of these icons should be the network service. If it's using a wired connection, it will show an arrow going up next to an arrow going down. If it's using a wireless connection, it will show a fairly standard Wi-Fi icon that also indicates signal strength. If it's offline (or networking is disabled), it will show an outline of the standard Wi-Fi icon without any bars. If any of these icons show up, you can access additional settings by clicking on it. Perhaps your issue is as simple as enabling networking or changing a few of those settings.
But for the remainder of this answer, I will proceed with the assumption that you are having a similar problem to the one I encountered a few weeks ago, which made the network indicator disappear entirely. So if you can see one of these icons and clicking on it brings up some network-related options, you can just skip the rest of this and let me know what it looks like.
A few weeks ago, my work computer (running Ubuntu 14.04) randomly decided to be completely offline. It looked like the network manager service did not start at all, and starting it manually didn't help. If you're experiencing a similar-looking issue, I would start by trying to restart the network service. Run sudo service network-manager restart
in the terminal. If that restores the network icon, then that may have fixed the issue. If, however, the icon is still missing, follow the instructions on this question's answer.
About this bug
Ubuntu uses, among other things, some libnl packages for certain networking functions, and there was a proposed update to these packages that had some compatibility issues with the network manager service. This should only affect people that have enabled proposed updates, although I don't believe I had enabled this setting, so I'm not sure how it affected me. Regardless, it apparently did, and following the instructions linked above fixed it for me. Note that you should also be sure you place a hold on the packages so they don't get updated until the bug is fixed either with a libnl update or a network manager service update (instructions at the link above).
lspci -knn | grep 'Eth|Net' -EA2
terminal command. – Pilot6 Jun 08 '16 at 19:27