Many decades of intensive astronomical research has revealed a wealth of data on how stars form.
“Star formation is the process by which dense regions within molecular clouds in interstellar space, sometimes referred to as “stellar nurseries” or “star-forming regions”, collapse and form stars.” Source Wikipedia
Although the broad aspects of how this happens are now clear, the fine details are not. A 2018 paper in Nature Astronomy drew attention to one particular aspect - the relationship between the mass of star-forming clouds of dust and gas and the eventual mass of the star itself.
“Understanding the processes that determine the stellar initial mass function (IMF) is a critical unsolved problem, with profound implications for many areas of astrophysics.”
A series of new experiments are currently being conducted aboard the Stratospheric Observatory for Infrared Astronomy (SOFIA) with the aim of revealing more details. The BBC's 'Sky at Night' programme recently covered star formation (9th Dec. 2018) and described the German Space Agency's DLR 'German Receiver for Astronomy at Terahertz Frequencies'(GREAT) which is looking at the extreme lower end of the infra-red spectrum to find clues.
Professor Chris Lintott (BBC) “We've known the basics for a long while, but the details are still very obscure. We don't understand them.”
Karl Jacobs (DLR) “That is absolutely right. So that is what we are looking for - and finding new things every day.”