How did the universe form?

There are a number of theories that attempt to explain the origin of our universe, however, the Big Bang Theory is the most commonly accepted model.
According to the Big Bang model of our universe, it all started from an infinitesimally small point (a singularity) in space. In a very-very short span of time (much less than even a fraction of a second), the universe expanded at a rate faster than the speed of light itself. The expansion of our universe is still continuing, however, the speed of expansion is very slow as compared to the beginning.
It has been hypothesized that as the universe expanded and cooled (as compared to its initial state), various elements were formed and over time, stars, planets, and other heavenly bodies were formed.
The discovery of the cosmic microwave background (CMB) in 1965 is the conclusive evidence of this theory.
Hope this helps.