don't
How to play for a draw?
Go for a closed position, keep trading until endgame. And when winning, offer draw unless there is VERY little material on the board. 3rd to advise that lol.

Always (win or draw) play for active pieces, but to draw, at the same time minimize anything dynamic. Like pawn structure for example, ideally you can keep it symmetrical. Trade often, but not at the cost of activity.

Does that mean that you need to play for a win even if you're actually hoping to draw – and when you would otherwise have kept playing to secure the win, you just offer a draw instead? (Sorry, this question is stupid, but I have no idea how to play if I aspire to draw a game.)

Does that mean that you need to play for a win even if you're actually hoping to draw – and when you would otherwise have kept playing to secure the win, you just offer a draw instead? (Sorry, this question is stupid, but I have no idea how to play if I aspire to draw a game.)
It's kind of like the "shoot for the moon; even if you miss, you'll land among the stars" thing. Play your best, and if it's not good enough to win, then hopefully it will be enough to draw.
If you're fine with a draw, don't take unneccesary risks, but just trying to trade everything at all costs will help your opponent outplay you - because then they'll be playing moves because they think they're the best moves, and you'll be playing moves to "trade stuff."
Honestly though, your rating is too low to be thinking about this stuff. Even players higher rated than you are very, very beatable. Playing for draws will just short-change your long-term chess development. I don't think "playing for a draw" is really a relevant concept until expert/master, or at least class A.

Does that mean that you need to play for a win even if you're actually hoping to draw – and when you would otherwise have kept playing to secure the win, you just offer a draw instead? (Sorry, this question is stupid, but I have no idea how to play if I aspire to draw a game.)
Yeah, I think that's where the snark comes in. When it's implied that you offer a draw in a possibly winning position.
The truth of the advice is that against a stronger player your position will likely deteriorate as the game goes on, if only a little. This means if you want an equal position, at some point you'll need to have an edge. Also, in a psychological sense, it's difficult to fight hard on every move if what you have in mind is a boring position leading to a draw.
Study endgames.
Trading pieces, keeping your pawns safe, letting your opponent come to you and always on a lookout to trade queens can help you to get a draw. It won't always be so because either you or your opponent is going to make a mistake but it does work at times. A bit advanced way would be to look out for perpetual checks.
But all that would go down the drain if you dont know basic endgames. Your opponent will easily cream you in a seemingly equal position if you are not careful.

To play for a draw even at above the 2200 level, you should play for a win.
By this, I mean make the best possible moves you can make even if they are a little risky. Do not try and trade down--this often leads to a loss.
For players under 2200 they really should not play for a draw.

To sum up, play for a win, keep the initiative, be careful not to make a silly mistake and if they offer you a draw when they're worse, decline it. Offer a draw yourself when you're slightly ahead.

First choose a drawish opening instead of all those sharp Sicilians and Ruy Lopezes and Pircs that most people play. Play an opening like the Petroff, Four Knights, Symmetrical English, Queen's Gambit Declined, or Exchange French, where the pawn formations are perfectly balanced and early queen trades are facilitated. Make your main goal to align pieces and pawns so that they have no good plan or future other than to get traded off. In my experience the draw typically comes about from one of these: (1) perfectly balanced pawn formations with an obvious endgame play for both sides, (2) a permanently locked position where pairs of bishops can't do anything useful, (3) opposite-colored bishops; (4) repetition, especially by a Pendulum Draw.
Here's an example of a type (2) draw:
Here's an example of a type (4) draw:
----------
(p. 179)
Pendulum Draw A draw by repetition when two attacking
moves are repeatedly played and answered by two defending moves,
with the same moves "swinging" to and fro. If the players do not agreee
to a draw, the game ends in a draw anyway by threefold repetition.
Pandolfini, Bruce. 1995. Chess Thinking. New York: Simon & Schuster.

Get a winning position and offer him a draw.
Edit - Wow, two people with the same snarky comment.
I don't think that is snarky at all. Had a tourney game this last weekend where I offered a draw in a pretty even position (materially at least, though I had more space and better activity); my opponent was 250 350 points higher than I was.
Later, I was up a couple of pawns and then my opponent offered me a draw. I ended up taking it since it was much more likely I would mess something up in the ensuing endgame.
So, playing for and getting a winning position and offering a draw is a decent strategy, especially if your opponent is generally much stronger than you (by rating for example). That is assuming there isn't a forced win on the board.
Against stronger oponnents.