Recently I've been trying to connect a cable between the router and my notebook but it doesn't recognize the connection. Please, help me to do this trick.
It should just connect automatically. You shouldn't actually need to do anything. The fact is is not connecting suggests that, maybe, your on-board ethernet port is not being recognized by UM.
The next step would be to Install "hardinfo".
sudo apt-get install hardinfo
It is like MS Windows' old "System" window where it lists all of your on-board devices. Even ones for which you do not currently have a driver. On there, you should be able to see if your ethernet is being recognized and if there is a driver installed. It'll probably be listed under the sub-heading of "PCI devices".
Hardinfo is listed in your menu as "System Profiler and Benchmark". You should find it under "tools" or "system" following installation.
Using top panel menu select:
System > Preferences > Internet and Network > Network Connections
In the Network Connections dialogue click 'plus', i.e. 'Add a new connection' button select 'Ethernet' type, and continue to the new connection configuration.