Here are a few still from the 1977 Rankin/Bass cartoon adaptation of The Hobbit, which illustrate the way some of the dwarves were portrayed.
Fili and Kili
Nori and Ori
Dori and Nori
Oin and Gloin
I am not a booster of this version of The Hobbit, which has many, many flaws, both as an adaptation and as a work in its own right. However, it's interesting to see how the animators dealt with the question of how to differentiate the dwarves visually from one another. I'm not sure they succeeded as well as they ought to have, but I think they did well enough, especially given how little Tolkien himself differentiated between many of them. Of particular note are Fili and Kili at the top of this post, who, I think, nicely convey being younger than their companions while still being recognizably dwarvish. (I also note that, as in the book, they are both blond and have long noses)