I moisten the exposed membranes with a wet q-tip and then sliding the tweezers between the shell and membrane if you can, (it's harder to do at the pointed end where it's more compressed together), and chip just the shell going up the egg. Moisten any membranes you expose. When you moisten the membrane this will also let you see how much veining is left. If there is a lot of veining, especially thick veins, you aren't going to be able to do much because it's not ready. If you hit a vein and cause bleeding, I hold a wet q-tip against it for a bit to staunch it and then replace it to the bator. If there's still heavy veining I wrap a damp paper towel around the back of the egg and put it back in the bator. If the veining looks about gone,(you can pull the membrane back) continue for 10 minutes or so and replace the baby to rest and warm back up and see if it makes progress on it's own. If it doesn't give it half an hour to an hour and so a little more work repeating this until it's out.
That's how I do it.
Some people use bacitracin/vaseline or non pain relief neosporin spread thinnly over exposed membranes to keep them from drying out as well.