How to soundproof window?

Short of REPLACING the windows, you don't have a prayer of blocking the sound of sirens. Even then, you can dampen the sound. but you won't completely sound-proof a window.

They won't be leaving the station with sirens at night. 

They have no need for them.

Move.

More characters.

You can't 'soundproof' it, but you can mitigate the noise to some extent. Ensure all the gaps are draught stripped (sound travels through air) and keep the window shut. Hang heavy curtains - eg velvet with linings and wadding interlining, the thicker the better and extending generously all round, down to the floor is best.

I assume your concern is at night when you are sleeping. If that is the case. Go to the drugstore and get some of the wax earplugs designed. to keep water out of swimmer's ears. My used them for many years and they were very effective

nothing is going to work.  the FD' siren is intentionally that loud.  forget it

Spend the next week looking for a new apartment.

SOL.  You could try some rigid foam from Lowes but the sound will just go thru your walls

   Either move or eventually get used to it.

Sound will carry through walls and there is NO way to soundproof. Also, in an apartment, you cannot glue or permanently change construction.

A window is normally recessed and you can fill the space with material.

The walls may take mounting of strips later removed.

You can buy small amounts of sound proofing and sound absorbing foams

https://www.soundproofingtips.com/soundproofing-ma...

It's the best you can do other than moving.

need to add another 'layer' of glass, like a storm window.   IF you don't use the window that often, just some heavy drapes will help.