While digging through the book to answer a question about the time limit on the games, it seems that a typical length was several weeks:

The twenty-four tributes will be imprisoned in a vast outdoor arena that could hold anything from a burning desert to a frozen wasteland. Over a period of several weeks, the competitors must fight to the death.

However, I do not recall any other mentions of the length of the Games. Is there any canon source that gives an exact duration of the 74th Games?