White is a pawn from queening, has the enemy king cornered, and has just drawn the game.
Black has no legal move and is not in check, so the game ends there, drawn, and the extra pawn counts for nothing. Half a point each, written ½-½ on the scoresheet and on the crosstable.
There are seven ways to reach that half point, plus one clock rule that behaves like an eighth. They sort into three piles: the draws that end the game the instant the position appears, the two you have to claim, and the two an arbiter applies whether anybody asks or not.
The three that end the game on the spot
Stalemate is Article 5.2.1 of the FIDE Laws: the player to move has no legal move and is not in check. No claim, no handshake, no arbiter. The position above is over. It is also the single most expensive rule in beginner chess, which is why there is a whole page on what stalemate is and another on how to avoid it.
A dead position (Art. 5.2.2) is one where no series of legal moves, however awful, could produce a checkmate for either side. The everyday version is running out of pieces.
King against king, king and bishop against king, king and knight against king, and king and bishop against king and bishop with both bishops on the same colour: those four are finished the moment they appear. Insufficient material covers the details, and dead position covers the stranger cases, such as pawns locked so hard that nothing can ever be captured again.
The third instant draw is agreement. Both players have to have made a move, then a handshake ends it (Art. 5.2.3). There is an order to doing it properly, and draw by agreement has it.
The two you have to claim
Threefold repetition (Art. 9.2) and the fifty-move rule (Art. 9.3) are rights, not events. The position can repeat five hundred times and the game goes on until somebody with the move claims.
The same position three times, with the same player to move and the same castling and en passant rights, is a draw on request. The three appearances do not have to come one after another. Threefold repetition explains what counts as the same position, and it is stricter than it looks.
Fifty moves by each player with no capture and no pawn move is the other one. Any capture, any pawn push, and the count goes back to zero. Fifty is generous: king and queen against king is ten moves at most, king and rook sixteen, bishop and knight thirty-three. See the fifty-move rule.
Claiming either one has a procedure, and getting it wrong hands your opponent two extra minutes. You must have the move. Either the position has just appeared and you say so before touching a piece, or it is about to appear, in which case you write the move on your scoresheet without playing it, stop the clocks and call the arbiter. Play the move first and your claim is gone, because the position on the board has changed.
The two that happen without you
Since the 2014 Laws, an arbiter ends the game after a fifth repetition, or after seventy-five moves by each player with no capture and no pawn move (Art. 9.6). Nobody claims. Nobody can decline. The only exception is checkmate: if the seventy-fifth move happens to be mate, the mate stands. These exist so that a game cannot be dragged out by two players who both refuse to be the one who asks. The 75-move and fivefold rules has the rest.
The clock rule is the eighth. Under Art. 6.9 a flag fall normally loses the game, but not if your opponent could not mate you by any possible series of legal moves. Your flag falls and all he has is a king and a bishop: draw, not a loss. And if all he has is a king, it is a draw no matter how much time you have left, because a lone king cannot win.
The draw you will meet most often
Not any of those, in practice. It is perpetual check: you are lost, you find a queen that can check on two squares forever, the enemy king shuttles between two others, and neither of you can change anything. That is not a rule of its own. The draw arrives as a threefold repetition or a handshake, once both players can see the checks will never stop. It has saved me more half points than every other rule put together. Perpetual check has a board with the checks played out.
One last thing, because it is where the half points actually go at club level. Almost every draw I have watched a junior hand over was a stalemate in a completely won position, usually with a queen still on the board. Learn king and queen against king properly, and get into the habit of counting the enemy king’s squares before every quiet move: if the answer is zero and you are not giving check, you are about to draw. Ten minutes of queen endgame puzzles a week makes that automatic, and it is the cheapest half point in chess.