Babies deliver themselves. Women automatically feel the need to push. How you can confuse a women in active labor for a women with only a simple cut to her leg, I don't know. I don't mean to insult anyone, but your friend seems fairly clueless to not recognize that her complaints of pain weren't consistent with a leg injury (unless it was a quite nasty leg injury).
Bare minimum info: Call 911. There is lots of bloody stuff that may gush out. Catch baby (even if you don't know how to maneuver the baby's shoulders out, the baby will still come out after some pushing unless there is a complication). Clean out baby's mouth and nose so baby can breathe and cry. Crying is good, silence is bad. Most babies are bluish at birth. Clamp off cord. The placenta will detach and deliver itself soon thereafter.