Freestyle- Both the arms and legs may be used to execute holds or to defend against the attack. If legs are used as part of the attack by an aggressor, then the wrestlers return to standing. If throw from standing is blocked then, the attacker receives 2 points + position choice.   
  Greko Roman- A wrestler may not attack an others legs nor use his own to trip the wrestler must wrestle from standing without the top of his head against his opponents chest. This is called "passivity", and will result in a call of "contact" by the official. The official will say," contact red", or "contact blue", before actually indicating a passivity by holding an opponents palm in the air with the offenders color  indicated. The match can end by regulation, pin ( both shoulders are held on the mat ), 10 pt. margin, or injury default .     
  Folkstyle- In folkstyle both legs and arms are used. You are not allowed to throw punches or put scissors in like some people think. You start standing called "neutral".  When in this position the object is to score a takedown. To do this a wrestler takes a shot and can't tackle or pick the opponent up and throw him. When starting from referees position the wrestler is either on top, or bottom. When on top you are allowed to take an ankle to break the the bottom guy down, but if if he stands up you're not allowed to lock (touch) hands below the waist. When on bottom the wrestler has to stand up, or get a reversal.