Seems like when they are first "switched on" they start writhing around and the egg tooth makes slits in the eggshell wherever it hits. I don't think they necessarily aim up, at the very beginning anyway. Then in the process of pushing around, their head pops out. That's what it looked like to me when I've observed it, at least.
I've sat fascinated as I watched one make slits by pushing all over on the egg from the inside, and then the head just shot out when it pushed on an opening. They then sit there and start breathing. I think for at least some length of time they're getting oxygen both from breathing and gas exchange through the eggshell into their bloodstream, at least until the connection breaks. (I wonder at what point the umbilical cord physically disconnects?)
Sometimes they get egg "goo" covering their nostrils and you can see that they are simply breathing the same air in and out of the bubble. It's pretty funny. Maybe we'll catch one of them doing it this year.
No, I'm not excited at all...