Left with King /Oponent 3 or more pieces

What is the rule after, for example, I'm left with the King only and my opponent has a Queen, a rook and any other piece. Is there a specific number of moves, my opponent can make,  before declaring stalemate?  

50 moves without a capture or pawn move and the game can be declared drawn. Any capture or pawn move resets the count.

Thank you. I assume that the 50 moves includes both players  

Yes, the 50 moves includes both players in that both players have done 50 moves without capture or pawn move. After 50 moves have been done with no capture or pawn move any of the players can claim a draw when he has his turn. If he makes a move instead the game goes on. Then the other player can claim the draw if no capture or pawn move was done when the first player moved. If the second player moves but no capture or pawn move was done the first player can again claim the draw and so on. As long as the draw is not claimed the game continues. If a player makes a capture or pawn move the count resets as Martin_Stahl said and it will take another 50 moves without capture or pawn move before a draw can be claimed.

Stalemate is something different and can not be claimed. Stalemate happens when a player has his turn but it is not possible to make any legal move and he is not in check. That ends the game right away and it is a draw.