Never help a chicken out of the egg if you can help it. You will end up doing harm than good, and the ultimate is that you could end up killing the chicken or it could just be a weak specimen that will never thrive. The very opposite of your intension.
Remember at all times, Darwin's law - survival of the fittest. In hatching eggs you will always have those that don't make it. Let nature take its course, as hard as it is at the time. You will find people who will tell you that it is okay, it really isn't. And if you have a deformed chicken, it would be best if you did not interfere.
What I can say is this, that chickens can take the whole day to emerge from their shell after you hear them pip. However, if after 12-14 hours they haven't emerged, you can then help them out as they will probably die one way or the other, but by this time you are giving them a fighting chance.
However, it should be done really carefully and over a couple of hours, in order to mimic nature as closely as possible.
Making sure that the room is warm, take the egg out of the incubator and try and prise away the egg shell without disturbing the membrane around the pipped area. You can do this with a pair of tweezers, a toothpick or the blunt end of a needle. It should be done in small bits and the way to do this is to take one end of the egg and squeeze gently so that the egg shell crazes into small pieces.
Never disturb the membrane at this stage as if you do there will be blood if you go through the membrane, which you don't want. If you don't stop at this stage your chicken could bleed to death.
If, by some chance of bad luck you do end up in this situation, take a warm, wet handcherchief or facecloth and wrap the egg up and put it back into the incubator. However, while doing this make sure that the hole is not completely covered as the chicken is breathing air at this stage and needs to have access to it.
Also make sure that when you put the egg back that the pipped area of the egg has been placed facing up or on its side, and not face down. Leave it for at least half an hour and start again.
Remember that the chicken egg has 3 layers; the shell, the outer membrane and the inner membrane that carries the blood supply to the chicken. The reason why your chicken is not having a good time hatching could be from a number of reasons, but the main reason is lack of humidity which dried out the membranes and the chickens then have difficulty getting out.
Once you have removed most of the shell, wrap the chicken covered in the membrane in a blood-warm hot, wet cloth to soften the membrane. Leave for about 15 minutes. Don't cover the beak area.
If you notice that the shell is stuck to the chicken in places this is a confirmation that the humidity in your incubator was too low. Don't remove the shell that is stuck. The chicken should be able to help itself at this stage. You also don't know if the chicken as absorbed all the yolk sac or if the blood flow is still flowing.
You can raise the humidity level in your incubators by putting in very hot, steaming face clothes and replacing every half hour.
Remove the egg again and see if the chicken can emerge on its own at this stage. If not, tear the membrane because at this stage there is very little hope either way. Once it has emerged put it back into the incubator to keep warm.