How do I know my system is infected with Trojan viruses and how do I get rid of it?

Very generally, you can tell if you are infected with viruses or malware by your system speed. If you are experiencing increased processing times, see processes running that you did not initiate, or see your system exhibiting odd behaviors, there is a good chance that you have been infected. A good anti-virus program should help you to debug, although you may have to run it several times. Be sure to keep your anti-virus updated and to not engage in risky online behaviors once you are up and running.

You can run it by Virustotal: https://www.virustotal.com/