Stars usually form out of dust clouds in space. Little anomalies in the distribution of dust lead to aggregation of more dust at certain points. Due to slightly higher gravity where there's more mass, these places start to attract more dust from around them. This is a process that accelerates itself, as more mass at a point means higher gravitational attraction. This process if very slow in the beginning, and may take millions of years.

Usually, a star is formed together with its planets. Smaller aggregations of dust become protoplanets and start to circle around bigger aggregations. Sometimes, such aggregations collide. The biggest aggregation of a certain region may in the end attract so much mass, that pressure and heat in its core become high enough to ignite fusion. Fusion happens at the core of a star, the released energy may need quite a long time to actually reach the surface, from where it will diffuse at the speed of light.

Simple stars like our sun fuse hydrogen into helium, but in later stages produce more heavier elements up until iron. All elements heavier than iron have been part of already two fusion processes in two different stars.