How did astronomers discover how stars were formed?

As you can imagine, there is nothing attached to a star that says 'I am 10 billion years old', or, 'I was just formed 1000 years ago'. To get this kind of information, astronomers have to use logical deduction based on a collection of clues they have accumulated over the decades. To form a star, you require a more primitive condition where the matter is present in another, more distributed form. This describes interstellar gas clouds and nebulae to a T. By examining nebulae, astronomers find objects that are starlike, but display many spectroscopic properties that suggest violent gas infall or outflow, as if material is flowing into a region of high density. These objects are commonly so deeply embedded inside the clouds that you cannot see them with optical telescopes, but have to use infrared telescopes to detect them. One dramatic infrared picture of a dark nebula in Orion, shows dozens of optically invisible, star like objects glowing brightly in the infrared. By looking at many different clouds, astronomers see objects with different properties, and they can order them in a rough chronology. The invisible infrared sources eventually 'turn on' and become full-fledged stars, and in several nebulae we can see these infant stars as 'T Tauri' objects. These are typically stars with the mass of the sun, partially embedded in nebular material, but showing tremendous chromospheric activity, flares, powerful winds etc. After about 10 - 50 million years, the star becomes far less active and we think this is because the gas and dust in its fetal environment has been blasted away or evaporated.

Again, the trick is to look at as many different nebulae as we can to find additional 'stages' in this formation process. We know that for massive stars, the formation process is vastly different than for stars low mass stars like our sun. Astronomers use the laws of physics to interpret the data, and to organize the observations into physically consistent evolutionary sequences.