Answer:
It takes billions of years for molecules of Hydrogen, floating around in space, to come together in sufficient mass to eventually coalesce into a protostar (the first stage), it usually takes another event, such as the shockwave from a supernova to give it the "nudge it requires", allowing gravity to come into play, for this to happen.
But that's only the beginning. Another 100,000 years or so later, when the protostar has gathered all the gas that it can, it becomes a very hot ball of gas called a T Tauri star. It still doesn't have enough mass, and hence pressure, to begin internal nuclear fusion, even though it can appear as bright as a regular star.
It's going to take gravity around another 100 million years to collapse the T Tauri to the point where it's core can begin nuclear fusion. This is the point at which you can say that the star is 'born'.