The theory of the Doppler shift is something that all of us are familiar with (even if you don't know the scientific name for it). The most common example of this is of an ambulance passing by a pedestrian. The pedestrian can hear the siren as it approaches. As it passes, however, the pitch of the siren appears to lower. This is the same effect heard on Formula One racing tracks when the cars pass the microphone.
The scientific explanation for this is not that complicated. The siren on the ambulance creates a series of waves in the air that when put together make up a sound wave. As the ambulance approaches, the pedestrian hears the waves 'squashed', as the movement of the object raises the frequency (making the note the pedestrian hears appear higher). When the ambulance passes and begins to move away the pedestrian hears the waves 'stretched', decreasing the frequency (making the note appear lower).
Edwin Hubble realised that this theory could be used to work out how fast stars and even galaxies were moving away or towards the Earth. As light itself is a wave, the Doppler shift applies to it. An object moving away from the Earth1 would appear to emit a lower frequency of light, making it look redder (known as a redshift). An object moving towards the Earth would appear to emit a higher frequency of light making it look bluer (a blue shift).
Hubble measured the spectrum (light levels at different frequencies) of hydrogen2 from distant galaxies. He was amazed to find that almost all were redshifted and therefore moving away from us - and at fantastic speeds. Furthermore, he discovered that galaxies further away from the Earth were more redshifted, and therefore moving away faster.
Using this information, the 'clock' could be wound back, meaning that the universe must have originated from a single point. This single point cannot be defined to be the centre of the universe as the entire universe was present in this point. The best way of describing this is like the skin of a balloon. As the balloon is inflated, the points on the skin all move away from each other, with no point defining its centre. The universe behaves in this way only with more dimensions. This is the theory of the Big Bang.
The remnants of this can still be seen today. 14 billion years ago the Big Bang emitted large amounts of light as it was at roughly a billion degrees Kelvin (absolute measure of temperature - 273°K = 0°C). Light from 14 billion light-years away is still reaching us today, and so we are still being showered with light that has come directly from the Big Bang. The particles emitting this light however are travelling away from us at almost the speed of light - as they are almost on our event horizon - making the light they emitted highly redshifted and their temperature appear much cooler (only 3 Kelvin!). It is now only perceptible as a faint microwave background radiation, which we are familiar with as white noise on un-tuned televisions.
The Hubble Constant
Galaxies further away from the Earth appear to be moving away faster than closer ones, and so Hubble theorised that a constant is involved:
As you would expect the furthest 'detectable' objects in the universe to be receding at the speed of light this constant can then be used to calculate the size of the universe:
Now dividing this size by the speed of light should give its age (how long it took for the furthest 'detectable' objects to travel that distance):
The closest estimate for the age of the universe is 14 billion years.