Light being red-Shifted
When we look at light from distant galaxies, they have a lower frequency than they should have. This means they've shifted towards the red end of the spectrum.
More distant galaxies have greater red-shifts than nearer ones, so they are moving faster away.
This provides evidence that the whole universe is expanding.
We have detected low frequency electromagnetic radiation coming from all parts of the Universe.
This is mainly Microwave.
It's known as the cosmic microwave background radiation.
This is strong evidence for the Big Bang theory, as it shows the Universe expands and cools and drops in frequency.
This lead to the Big Bang Theory being the currently accepted model.
Something must have started all of the galaxies moving away from each other, maybe the 'big bang'.
All the matter and energy must have been compressed into a very small space that exploded and started expanding.
This expansion is still going on.
The big bang may have happened about 14 billion years ago. Though this isn't very accurate.
The Steady State theory:
This is the belief that the Universe has always existed and it will always be here.
It explains the expansion by suggesting matter is being created in the spaces as the Universe expands.