You don't need a telescope to see it, you just need to be somewhere where the light isn't so present already that it blocks your view of it. This is our galaxy, the one we're in and the one we see at night. You can look at it here or you can look at it outside at night if there're no clouds and no significant amount of light pollution, and when you look at it you'll likely notice that it has dark areas in it.
This observation of the night sky is where the term "dark matter" originated, and because I don't need a telescope to see it, it is one of the older terms that has been batted around for quite some time now.
We like to name things, so that our conversations have more meaning, and while we were looking at the sky and giving names to the different portions of it; "stars here" is the easy one because we have a star and we can see lots of other stars, and the places where there are no stars could not just be called "no stars here" because of what we know of stars, and that is that they give off light. There has to be "something" in the dark areas of what we see in this galaxy, because otherwise I'd see all of the other stars that I know are behind these dark areas.
So, because we knew that these areas are not stars, stars give off light, and that these areas actually blocked the light of other stars behind them, which means there has to be some matter there in order to do so, we named these areas "Dark Matter"
True story, and it was and remains one of those "fill in the blanks later as new information is gathered" type of stories to us, and as telescopes improved over time we actually have begun to fill in some blanks here. We've discovered and named Nebulas, places where Stars are birthed, since first naming the dark matter, and I'm sure as time goes by and electron microscopes get refined and pointed towards the sky, all of what isn't known here yet will become clear.