Check out the picture accompanying this post (courtesy NASA). It is a graphical timeline of the history of our universe. Let's walk through it step by step - from left to right.
Quantum Fluctuations: the universe starts off as a tiny blob of quantum fuzz, perhaps 0.000...thirty more zeroes...1 centimeters in size; basically out of void and nothingness - the uncertainty inherent in the laws of quantum mechanics (see post on the quantum world for more). The physics during this period is not well understood - it lies in the realm of String Theory. The temperature of the quantum fuzz is 1000…plus twenty more zeroes degrees… at these temperatures, all the laws of physics are expected to be highly symmetric and the forces of Nature unified.
Inflation: the random quantum fluctuations get frozen out during a remarkable period known as Cosmological Inflation: a violent expansion of the universe driven by the repulsive force of dark energy (see post on Dark Energy for more). This lasts only 0.000…thirty or so zeroes…1 seconds; but it is so violent that, at the end, the universe is only about 100 times smaller in size than what we see today! The explosive expansion cools down temperatures to a comfortable 1000…fifteen more zeroes degrees.
In the next few seconds, the expansion continues but slows down dramatically (see comments about the graceful exit in another post). The laws of physics loose their symmetric form and the force laws start fragmenting into different branches, as we see them today: electromagnetism, gravity, weak force, and nuclear force. Protons and neutrons form first, then Hydrogen and Helium as the matter condenses out of the vacuum into a cooler universe. By the time we reach a few hundred thousand years since the beginning, atoms abound and the stuff in the universe goes from opaque to transparent: that's the point labeled Afterglow Light Pattern in the timeline. This is the Cosmic Microwave Background (CMB) radiation that we image today (see other post on the CMB for more). The temperature is now a chilling 3000 degrees.
The universe continues to expand and cool down at a slower rate for the next 14 billion years. We first go through the Dark Ages - when witches were burned alive and alchemy was common. Then we have the formation of the first stars about 400 million years since the beginning. Then we get galaxies, and finally here we are living our miserable lives.
This picture of the history of our universe crucially relies on that initial critical and delicate period called Inflation - when the universe underwent a violent expansion that stretched space faster than the speed of light. Without the inflationary epoch, it is effectively impossible to realize a universe that looks like ours today (see other post on the multiverse). The video accompanying this post gives an excellent and brief description of what Inflation is, including a discussion by the father of the inflationary theory, Alan Guth. Enjoy.