I just bought a new Samsung monitor and it has 1 stuck pixel. I tried applying pressure to it and it didn't do anything.

Did you apply pressure during a full power on/off cycle?
I don't know if that still works, It's been years since I have tried it. If captaincranky finds this thread, He probably knows the best remedy or things to try....he's a bit of a monitor expert.

So how exactly does this work?

1. Turn the monitor on to see the dead pixel
2. Press a damp cloth against dead pixel
3. Turn off monitor
4. Wait (for how long?)
5. Turn on monitor
6. Remove cloth

Do I have to press the dead pixel at the same time of turning monitor off/on, because I kind of need a hand to press the back of the monitor?

1) put pressure on the pixel
2) turn on monitor
3) leave on 1-2 minutes
4) keep pressure on pixel and turn off
5) wait 30 sec
6) turn monitor back on and remove pressure.

Thats how I used to do it.

**** if that does not work, do a very fast on/off cycle
Hope it works for you.

Memory Express actually took it back and gave me a new one, how nice of them.