We don't.
How do chess players sleep at night?

We don't.
There's gotta be some way to make the pieces go away ;-;
Medication...Heavy medication.

First, they draw a bath.
Second, they check what time they must be up in the morning to set their alarm clock.
Third, they make sure there is no opening to the doors or windows.
Fourth, they record their moves they must make the next day in their to do list score sheet.
Fifth, they decide to lose no time worrying about what they cannot control.
Sixth, they take the initiative to pull the covers down and get in the bed with their mate.
Seventh, they most certainly censored
Eighth,
They sing a tune...
"It's been been fun
and it's been
real
Ben-
a-
dryl"

First, they draw a bath.
Second, they check what time they must be up in the morning to set their alarm clock.
Third, they make sure there is no opening to the doors or windows.
Fourth, they record their moves they must make the next day in their to do list score sheet.
Fifth, they decide to lose no time worrying about what they cannot control.
Sixth, they take the initiative to pull the covers down and get in the bed with their mate.
Seventh, they most certainly censored
Eighth,
They sing a tune...
"It's been been fun
and it's been
real
Ben-
a-
dryl"

Shhh! That was the part that was censored! Just kidding. As much as the ego hates to admit it, you are right and I was wrong about that.

Thankfully, I haven't made it to that level yet, but a couple of years ago, on a Saturday, I devoted 8 hours straight to solving tactics trainer problems and managed to complete 1000 of them before becoming too tired to stay awake any longer. As I started to fall asleep, I would see chess problems over and over and then dreamed about them. I smiled because I knew I had successfully overloaded my conscious brain and my subconscious thought it was helping me to solve problems that were important to life while I slept because it couldn't recognize the difference between an urgent life problem or regular one I guess?
In any case, my sleep was sweet though weird and my rating started to improve the next day.

It's 11PM. I should definitely be heading to bed early due to the early wakeup the next day. I rest my head against my pillow, so relaxing as I feel the coolness against my cheek for a sweet precious moment. I pull the covers up closer to me as I bask in the warmth. My eyes start to droop and slowly close. It's a peaceful moment, one of which I would probably fall asleep to... until I am rudely awokened... 1. d4 d5 2. c4 dxc4 3. e3 Be6 4. Nc3 Nf6 5. e4 Nc6 6. Nf3
Hey look, my imaginary knight just forked that rook and king. Oh there's a mate in 3.... All of this playing out in my head in such a surreal manner that it almost seems real, were it not for the fact that this game is being played out by my head and vividly displayed in my mind every time I close my eyes.
I can't handle this and I sit up in bed feeling frustrated. I decide to try to distract myself and do something else productive such as finishing a book, or getting a glass of water.... But as the water pours into the glass.... Pawn to d4. Pawn to e4. Knight to f3, Bishop to c4, Knight to c3. Bishop to f4.
I sit there slowly looking at the glass wondering if the glass is being checkmated in 3. Eventually I crash and fall asleep, but my dreams are full of castling and en passant captures. There is no escape from this hell.
How the heck do chess players sleep at night?