Stalemate is not the only draw that can be achieved in the game of chess, although it is the most well known. The other two types of draws include the fifty-move rule and the three-fold repetition. If you are looking for the win then you want to avoid draws as much as possible and have the game result in a checkmate instead of a draw.
A stalemate is when it is your opponent's turn, but they have no legal moves that they can make. This means that the king is the only piece that can be moved, but it cannot be moved into check. Remember that it is illegal for a king to place himself in check. This results in the draw by way of stalemate. Neither player wins the game.
The fifty move rule is when there are no pawn movements and no captures for fifty consecutive moves. If a pawn move or a capture takes place, then the count resets to zero and begins again. Upon reaching fifty moves either player may claim a draw and again no one wins the game. Typically this happens when both players only have one or two pieces left on the board.
The three-fold repetition says that if the exact same position occurs on the board three times during a game, either player may claim a draw. Sometimes this is done on accident, other times it is forced by placing an opponent in check over and over again. Think of being able to take a picture of the board three different times during a game and the pictures come out identical to each other.
Try to avoid these draws so that you are able to come away with an official win. Avoid these by watching out for them and being sure to look for every opportunity to place your opponent in checkmate.