When does my opponent have to tell me if they will play first?
You must decide before looking at your first hand of the game, it can be after sideboarding. If you do not choose it is assumed you will play.

From the Magic Tournament Rules 2.2:


  For the first game of a match, the winner of a random method (such as a die roll or coin toss) chooses either to
  play first or to play second. The winner must state this choice before looking at his or her hand. If the winner
  states no choice, it is assumed that he or she is playing first. The player who plays first skips the draw step of his
  or her first turn. This is referred to as the play/draw rule.  
  
  After each game in a match, the loser of that game decides whether to play first in the next game. They may wait
  until after sideboarding to make the decision. If the previous game was a draw, the player who decided to play or
  draw at the beginning of the drawn game chooses.