Fill a bowl with warm but not hot water.
Place a washcloth over the bowl so it touches the water - but just barely. Think of it as a soft safety net for the chick if you can get it out of the egg safely.
Carefully lower the chick in the egg onto the washcloth and even more gently attempt to moisten the membrane at all points where it is attached to the chick.
Using another washcloth that has also been slightly dampened with warm water, fold it over the chick in the egg for a few moments and then remove it.
Repeat this process numerous times to weaken the membrane. This often requires extreme patience - at least in my opinion, but is essential to helping the chick hatch. Do not, under any circumstance, try to pull the membrane off of the chick, even if it appears to be smothering. Doing so can not only tear the chick’s tender skin but rip its veins.
You can gently try to break parts of the eggshell with tweezers, if it seems vital to getting the chick out, and to reach more membrane. If the shell will not crack easily that usually means the membrane is still too dry, and needs to moisten again with the cloth again - maybe multiple times.
You can use either the tweezers or your fingers to carefully and slowly detach only moistened membrane from the chick - if absolutely necessary because it is still struggling. ONLY do this with moistened membrane that lifts away easily.
If the water in your bowl starts to get lukewarm or cold, replace it with more warm water.
If you get a live chick out of the shell, gently wrap a dry washcloth around it so it does not get chilled, and pat it dry as thoroughly and quickly as you can.
Return the chick to the incubator as quickly as possible so it can get warm and stay warm.