Stalemate -- Your move. You are not in check, and you have no legal moves.
By Agreement-- A player may offer a draw at any stage in the game. The proper way to offer a draw is to make your move, offer the draw to your opponent and then hit your clock. Your offer is non-revocable until accepted or rejected by your opponent. This is done orally, or if your opponent touches a piece to make another move, your offer is rejected.
Triple Occurrence of position
Position has occurred 3 times before in this game. Position is the same if all the pieces are on the same squares, it is the same person's move, and the pieces have the same "powers" as before (right to castle, right to take en passant, etc)
To claim a draw, you should write your move down on the scoresheet (but do not make the move)
Stop the clocks
Make the claim
Insufficient Material to Continue -- Neither side can win with the pieces on the board. An example would be King versus King and a lone knight,
Insufficient Material to Win on Time -- You cannot win on time if you do not have sufficient material to force a win. EG You have a king and a single bishop.
50 Move Rule -- 50 moves have occurred without a capture or a pawn move.
To claim a draw, you should write your move down on the scoresheet but do not make the move)
Stop the clocks
Make the claim
Both players flags have fallen in sudden death and a player points this out.
Insufficient Losing Chances --
A player may claim a draw by insufficient losing chances.
In a sudden death time control
Where the players are using a clock without time delay
And the has less than 2 minutes on his/her clock
The claim will be upheld if his/her position is such that a Class C player could defend it for a draw against a Grandmaster if both players had ample time.
This claim must be made before the player's time expires.
The TD can grant, deny or ask the players to play on. The TD can also put the game under a time delay clock.
Things to keep in mind
Any draw claim is a draw offer.
If you have a question, ask the TD. That's what we're here for.
If you stop the clock to make an invalid claim, your time may be penalized.
Spectators should never discuss anything with players. You should not point out:
the fact that a player's time has expired
the fact that a draw claim can be made
anything at all except (perhaps) that the building is on fire.
The foregoing is based on the Fifth Edition of the USCFS rules. It is intended as a helpful summary. Obviously the language of the rules is the law, not my summary.