In our own galaxy (and other nearby galaxies), we see stellar nurseries in the hearts of giant molecular clouds (GMCs) - large regions of space heavily populated with gas and dust and cold enough for molecules to form. GMCs range in size from one to hundreds of lightyears in diameter and contain hundreds of thousands to millions of solar masses of material. The following is an image of the Orion nebula, which contains a GMC stellar nusery.
The GMC starts to collapse slowly. However, the cloud started out a bit lumpy (as most things in nature do), so those lumps will collapse more quickly than the other parts of the cloud. Why? Whenever you have a region of larger density, it will experience more gravity than other areas. This extra gravity will pull the lump together faster.
Each lump may, in fact, form more than one star if there is enough mass and if it is a lumpy lump. Each fragment that is on its way to becoming a star is called a protostar. During this stage, the collapse will cause the protostar to heat up, which will slow the collapse but not stop it. These protostars begin to glow, and can be detected in the infrared part of the EM spectrum - all other light will be absorbed by the surrounding gas and dust.
At some point, the protostar collapses so much that its core (the center region of the protostar) becomes hot enough to star fusing hydrogen into helium. At this point, the protostar becomes a full fledged star and enters what astronomers call the main sequence.
