From your profile it sounds like you almost certainly know more about astronomy than I do! I think that we know about different galaxies from the light that they emit.
I saw a TV show recently where they showed a picture of the universe with little specs of light that had travelled so far that they were thought to have first been emitted really soon after the big bang. That’s pretty cool isn’t it!
Soon after the invention of photography in the 1800s, astronomers starting taking photos through their cameras. What they could do is leave the shutter of the camera open for a long time, to see if they could pick up things that were too faint to see with just the eye and a telescope. What they saw amazed them. They saw hundreds of thousands of dots. Today, telescopes are much more powerful and see billions of spots, many in great detail. We can see galaxies of all shapes and sizes, and these can be classified into different types.
It tells you exactly how to classify the galaxies into different types. So far, over 60 million galaxies have been classified, but they have so many images that there is still lots of work to do. Have a go!
We can see other galaxies in the nearby universe with enormous telescopes, like the Hubble telescopes. So, whilst we can’t (for the moment) even hope to travel out of the Milky Way, we can detect electromagnetic radiation from galaxies outside our own, and the amazing pictures look like this: