How did people after taking a picture with film and doing the chemical processes, get that small film image to become a big picture that could be hung/framed before the invention of a digital scanner to blow up the image and print the image.
Going from negative film to a printed image is a two-step process. First, the negative is developed — the latent image on the film brought out and then fixed in place. Now you have a piece of translucent film with a negative image on it.
To go to a positive print, you then essentially repeat the process, shining light through the negative to form a focused image on photographic paper — paper treated with light-sensitive chemicals. The reversed negative image is reversed again, producing a positive print.
If your negative is large — as in large-format photography — you may make contact prints, where the negative sits directly on the paper. This results in an image exactly the same size as the original. If your negative is small (like 35mm film), you use an enlarger: a projector which shines light through the negative and uses a lens to focus the projection on your paper in the darkroom.
This is just the high-level view. The Wikipedia article for "enlarger" provides more — and there are many books and articles on the topic which are easily found now that you know what you're looking for.