For anyone that might not know the original Trojan Horse was given as a gift to the City of Troy by the Greeks who were losing the war but within this large wooden horse that was rolled into the gates of Troy was the Greek Army that came out at night when no one was looking and destroyed the city.
The PC virus variety of the Trojan Horse was first discovered in 2002 within sendmail and OpenSSH packages both included the Trojan Horse. It was made by a hijacker that broke into the distribution URL's and replaced the program with his own damaged and infected ones. That is one way that your operating system can be given a Trojan, through software downloads and installation.
The most common way that users are infected with a Trojan "software" is through the spreading of it through emails. The sender will send it to the recipient within an email attachment that might say something like “nudgirls.jpg” or something along those lines that will make you curious and open the file.
Another popular way that Trojan Horses have been spread to people is through the ever increasing instant messenger(IM) programs such as Yahoo Messenger, AIM, ICQ, MSN messenger, and IRC. The one key to remember about Trojans viruses is that they have to be triggered by some mechanism and will not spread by themselves. For example, you can have one in your email but you do not open the link then it will not mess with your computer.
A Trojan Horse, once on your system can do a few things. First, it is able to completely take over your computer and not give you access to any of your files. It is possibly search your system and monitor your usernames and passwords to various URL's and even has the "right" of getting your credit card numbers and sending all your private informations back to the creator.

The best way to keep your computer from receiving any type of Trojan Horse viruses is that of prevention. Never open files sent you by people you do not know because chances are that not only are these messages SPAM email but will have attached some sort of link or file that will create a Trojan on your machine. It is fine to run anti-virus program on a daily basis but the fact is that Trojans are created so often that your definitions for viruses might not recognize the newest Trojans that have been maded.
Trojans Virus are not the kind of program that you want to speculate with so you should get your computer checked right away and continue to be leery of opening files by users you do not recognize.