No Stupid Questions

It turns out that when light travels through the mostly emptiness of space, it can travel amazingly far without being significantly diminished. So we see galaxies the same way we see stars - you can see some with the naked eye, in fact, but to see detail you need a telescope. They come in somewhat different configurations, but generally look like this:

We don't know exactly how many there are, we have to estimate it, and the range of estimates is huge: between 100 billion and 200 billion!

How do we estimate it? By counting the galaxies in a teeny tiny area of the sky, and then multiplying by that fraction. There are an amazing number of galaxies that are viewable in an area of the sky the size of the head of a pin held at arm's length. It looks like this;

By the way, the galaxy at the top of this comment is eighty million light years away. That means the light were seeing from it now left eighty million years ago; we're seeing back in time.

Just so you know, you don't need special equipment to see another galaxy. If you have good eyes, you can just go to a very dark place and look up. A pair of binoculars definitely helps though.

https://en.wikipedia.org/wiki/Andromeda_Galaxy

There's actually a bunch of local galaxies that you can see with just a pair of binoculars, a small telescope, or a good camera and some time.

The Messier Objects are one catalog of things that are pretty bright in the sky that you can see with your eyeballs through any basic telescope or binoculars. The numbers don't really mean anything, they're just the order they were cataloged in.
https://en.wikipedia.org/wiki/Messier_object

If you check out the list, you can see that a lot of them are galaxies. If you spend a little time learning how to find them, you can see them yourself. -- Andromeda is M32.

Those are all part of the Local Group. Which are a bunch of galaxies that are all nearby and pretty easy to find with telescopes.
https://en.wikipedia.org/wiki/Local_Group

have you seen the Hubble Deep Field image?

it's a picture of a section of the sky "about the size of a tennis ball at a hundred meters" taken by pointing the telescope at a point that appeared completely dark over a period of 10 days. there are over 3000 galaxies in that image.

Thanks everyone for all the answers and explanations! I really appreciate you taking the time to break this down.

It’s honestly mind-boggling to think about the distances involved, how long that light has been travelling before it reaches us, and just how unbelievably many galaxies are out there. The scale of the universe is very hard to wrap your head around.

Others have already answered, but if you are interested in the topic you might also like this project: https://www.zooniverse.org/

With a good telescope, what may have previously appeared as stars, turns out to be a collection of millions of stars in a tiny secti9n of the sky.

Here's a very zoomable image of the sky. If you zoom in, you can see galaxies. If you then zoom out a bit you get a sense of how many there are.

https://www.legacysurvey.org/viewer#NGC%206339

Just look at this picture: https://esahubble.org/images/heic0406a/
This is my go to when my problems start to feel too big :D

https://share.google/Zi6I0bL9oUbmtiSFJ

To give some perspective.

We make the following assumptions:

1. We are not in a privileged or special place in the universe.
   1a. Therefore the universe should look the same from where we are as from almost anywhere else.
2. Supernovae emit a very reliable amount of light.
   2a. Therefore we can accurately tell how far away a supernova is by its light signature.
3. We can tell how far away distant galaxies are when a supernova goes off in them.

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.

We see the galaxies as they were however many years it took for the light to reach us.

Every time we look, we find something new because there’s both a LOT of stuff in space and because light from further away keeps eventually reaching us.

…but mostly it’s a very complicated guess with a lot of math based on what we’ve already seen. Truth is, we don’t know precisely how many galaxies there are, but there’s always a whole shit ton of them everywhere we look, so it’s reasonable to assume the number is pretty big. And getting bigger because, again, we keep seeing new stuff.

By pointing a telescope at them and looking. You can see some of the larger ones through a cheap home telescope for a couple hundred dollars.

Didn't you know that Stephen Hawking has counted them all?

/s