So how do we know black holes collided over a billion years ago?
Please splain that to me in religious dummy terms.
Light travels at a uniform speed and is considered the speed limit of the universe. Gravitational Waves are theorized as traveling at or near the speed of light.
So if you know the black holes are 1.3 billion light years away then it means the Gravitational Waves we see coming from it are at least from 1.3 billion years ago. Any light you see in the universe is from the past. Light from the sun for example is a look into the past as it takes about 8 minutes and 20 seconds for the light to arrive at Earth.
As for how the distance is measured, there are various techniques and for distant objects, it's usually based on what are known as standard candles. Type Ia Supernovas are the most common Standard Candle and basically they have a luminosity that is very predictable and you can calculate how far they are by calculating the amount of red shift in the light curve they produce. If you remember from Hubble, the universe is expanding and the Red Shift is the skewing of an object's light curve to higher wavelengths (Red wavelengths are higher and blue lower).
Not the most precise explanation but it's got the basics.