What actual observational evidence has been collected for star birth? My friend states that no one has actually seen a star being born, but I told him that observation over a long time in star birth regions would show a star shining one day when it was not there earlier. Is there anything like that?
I don't think anyone has ever observed a star "turning on" like a switch has been flicked. Even though star formation can happen quite "quickly" compared to other astronomical events, it still can take hundreds of thousands of years for a molecular cloud to collapse and form stars. That time scale totally dwarfs a human lifespan, so the likelihood of looking at the exact place in the sky where a star begins fusion, and looking with a powerful enough telescope, is extremely low.
That said, we have seen stars at every stage in their evolution, because there are so many of them! I like to make the following analogy: Imagine that you are an alien scientist visiting the earth for one day, and you need to learn about the life cycle of humans. You can't witness one human's whole life in one day, but if you observe many many humans at different stages of life, you could piece together how humans are born, live, and die.
With telescopes like the Spitzer infrared space telescope, which can look through dust clouds and which detects infrared light like that given off by stars even before they begin fusion in their cores, we can take stellar "baby pictures". (Check the Spitzer website for some spectacular examples)
For more information about star formation, check these links (the second one has cool videos of computer simulated star formation):
This page updated on June 27, 2015