According to the turkish penal code section 125, a person who attacks the honour or respectibility of another by insults, swearing or another attack their respectibility is punished by 3 months to 2 years in prison or a judicial fine. (three or more people must hear the slander)
You need to report the matter to The Jandarmerie, the Police or by writing to the public prosecutor (Cumhuriyet savcısı) within six months of the offence. If you have a witness or two, a case will be opened and the suspect punished.
After conviction you can open a case for damages at the nearest civil court.