In the short story, "The Most Dangerous Game" how was the main character Rainsford brave? And how was he smart?

Rainsford is a brave in two ways. First, he is a hunter.  In fact, he is a world renowned hunter.  We can deduce this from the fact that General Zaroff recognizes him and has even read his books. So, as a hunter, we can say that Rainsford is a brave man. 

Second, when he forced to play the "game" with General Zaroff, he tries his best.  At first he tries to hide, but then he realizes that he has to go on the offensive.  He does not allow the dogs, Ivan, or Zaroff who have the clear advantage get to his head.  Rainsford stays as calm as he could and even attacks them. In the end, he wins. 

As for Rainsford's intelligence, Rainsford uses his hunting skills.  For example, he makes a Malay man-catcher.  Zaroff even says that not many men know how to make this.  He also shows intelligence when he doubles back to Zaroff's house and attacks him there.  He know that Zaroff would not be expecting this move.