I’ve always wondered how astronomers can actually observe galaxies that are millions or even billions of light-years away. What exactly are we seeing when we look at them?
And when scientists say there are hundreds of billions, or possibly trillions, of galaxies in the observable universe, how do they know that if we obviously haven’t seen and counted every single one?


We make the following assumptions:
1a. Therefore the universe should look the same from where we are as from almost anywhere else.
2a. Therefore we can accurately tell how far away a supernova is by its light signature.
Therefore, we can map out and count the galaxies in our local area, and, using assumption 1, we know that the number of galaxies in our volume of space is the same as in every volume of space. Multiply the one by the other and you’ve got your answer.
This is a great comment, but just for completeness, the Type Ia Supernovae is only one part of the Cosmic Distance Ladder.
https://en.wikipedia.org/wiki/Cosmic_distance_ladder
We can start with small, easier to measure things, and work our way outwards to more and more complicated measurement techniques. Most of these techniques overlap each other and can be used to confirm our measurements.
One of the big unsolved questions in cosmology is that many of our measurements disagree, this isn’t a “problem” just an unsolved question, and as a result, we don’t know how far away things are to the accuracy we would like. That being said, we still know how far away they are to a pretty damn close approximation.
The interesting thing is, the better we get at measuring how far away things are, the more our measurements differ from each other. There’s a lot of reasons why this might be, but one of them is that a Type Ia Supernovae might not be as standard as we think it is.
https://en.wikipedia.org/wiki/Hubble's_law#Hubble_tension
I chose a simple standard candle for a quick explanation, but yes, these are all independently verified by other methods, which in turn verify each other etc. Parallax is a good one: at one side of the earth’s orbit and the other, you measure the relative position of the thing you want to know the distance to, which is just like closing one eye then the other. Distant objects move less in your vision/against the background stars than close objects do.
For folks that would like the cosmic distance ladder explained in video format, 3blue1brown sat down with Terence Tao: https://www.youtube.com/watch?v=YdOXS_9_P4U
Yes, it’s that Terence Tao, the famed mathematician.