A hand comes across the board while your clock is running and a voice says “draw?” just as you were about to work out whether the knight is trapped. It is legal, it is not good manners, and Article 9.1 has something to say about the order of operations.
Move, offer, press
The sequence in Art. 9.1.2.1 is: make your move on the board, offer the draw, then press your clock. Doing it that way puts your opponent’s decision on their own time, and it stops the offer being used to buy a few free seconds or to fish for a reaction before you commit to a move.
Say it in plain words. “I offer a draw” is enough, loud enough for your opponent and quiet enough for the board next to you.
No conditions. “A draw if you take on d5” is not an offer, and the Laws say so.
Then write the symbol (=) on your scoresheet next to the move, which Art. 9.1.2.2 asks of both players. Almost nobody at club level does this, and it is the only written record if an arbiter later has to work out who offered what and when.
An offer made at some other moment, while your opponent is thinking or before you have moved, still counts as an offer. It just carries a risk with it, because Art. 11.5 covers annoying your opponent, and a badly timed offer is one of the ways people do that.
You cannot take it back
Once the words are out, the offer stands until one of four things happens: your opponent accepts, refuses out loud, refuses by touching a piece with the intention of moving it, or the game finishes some other way.
So the sequence every player learns the hard way goes like this. You offer. Your opponent thinks. While they think, you spot the move you missed, the one that wins a piece. Too late. They can accept, and the game is drawn, and you sign the scoresheet.
Look for the win before you look for the exit.
When not to ask
Three situations where I tell students to keep quiet.
When you are worse. The offer says you are frightened, and it tells a decent opponent to keep pushing.
When you have already offered once. Say it a second time and you are no longer offering, you are pestering.
When you are winning but short of time. Offering announces that you do not think you can convert it, and it invites your opponent to sit there and let your clock do the work. Play the increment instead.
There is also the case where the choice is not yours: Art. 9.1.1 lets an event’s regulations forbid draw agreements altogether, or before a given move, so read the entry conditions before you reach across the board.
And on the other side of it, the harder question is what to do when the offer comes to you. Below about 1800 my answer is almost always the same one: play it out. Taking quiet draws with anyone who looks strong is one of the quieter ways to stall at a rating, and there is a whole page on whether to accept.