Go get a free edition of Henry Peach Robinson's Pictorial effect in photography from Google Books.
Now google up a web site or two of great paintings. Many museums have a web site with a searchable collection. You don't need great reproductions of paintings, but you want decent ones. Poke around a bit until you can definitely find a bunch of pictures that you pretty much like, from anywhere between the 1400s to the 1800s. Sure, that's not all the paintings in the world, but they're the ones that will make sense in this context.
Skim over the little section of background I provide below.
Start reading Robinson. When he mentions a painting, use google to find a copy of it to look at before you read on, and take a look at the picture.
Keep reading until the end.
What you read will be somewhat dated, not everything should be taken as gospel truth. Robinson had some ideas about photography that are pretty old fashioned, and other ideas that are so modern that they are only now being viewed as acceptable (again).
When you get to the end, which should take a handful of hours, you will have learned more about composition than a 100 years spent on crummy web sites with their rotten Rule of Thirds and Golden Ratios, and their terrible terrible sample pictures.
Robinson was writing in the nineteenth century, when film did not exist. Emulsions were coated on to glass plates, instead. Exposure times were long, measured in many seconds, so moving subjects was a big no-no. People had to hold still. For portraits, a head-rest was used, to assist the subject in not moving.
Emulsions were also orthochromatic, which means that it was more or less impossible to take a photograph that included a decent rendering of clouds and landscape at the same time. The sky was normally white in a landscape photograph, without compositing together multiple images.
The long exposure times meant that shutters as we know them did not exist. One simply removed the lens cap, counted for a bit, and then put the lens cap back on.
Chiaroscuro means, basically, the arrangement of light and shadow in a picture.