Hi barbie. This is a very good question which I could not explain in detail during the chat. Here is a clearer explanation.
This was one of those questions that were in debate some time ago. Back in the early 30’s, an astronomer named Edwin Hubble was one of the first to have an idea of how old the universe might be. He was the one who realised that the universe was expanding, that each object was moving away from any other with a velocity proportional to their separation, that is
v = H D,
where v is the velocity a galaxy is moving away from us, D is the “proper distance” to the galaxy and H is known as Hubble constant. If you remember your Physics lectures, then you will notice that H has units of 1/time. So if H is constant then
t = 1/H
gives you an idea about the age of the universe. But that is not good enough, specially because measuring the Hubble constant has not been straightforward. Some good estimates would put this time between 12 -14 billion years.
Another way is to look at the life cycle of the stars. This involves a very good knowledge of physics and chemistry. I will not explain you how it is done because I am not sure how does it work. But the bottom line is that the estimates from this route tell us that the oldest globular clusters (massive accumulation of stars) are around 11 – 18 billion years old. Since these stars are part of the universe, then it cannot be younger than at least 11 billion years.
Then, there is the latest way. This time is by looking at the very first light emitted when the universe became transparent. Some people calls this an “echo” of the big bang. It is called the Cosmic Microwave Background (CMB) and it is a very dim glow everywhere in outer space (I talked about that here http://ias.im/47.739). By measuring some very fine details of this glow, we can determine the composition of the universe and its expansion rate very accurately. This allows cosmologists to estimate the age of the universe on 13.7 billion years, with an error of about 1%! This is true if our current ideas about the universe are correct… 😉