I should make this puppy a character of mine. Name him something stupid.

I picked some pretty extreme examples of expressions, but really this is about what you're trying to achieve best.
Try and focus exclusively on the eyebrows, eyes, and mouths of the puppy here if you're having trouble understanding how I translated the photos to a more simplified version of themselves. This is primarily what you're going for, and any detail you choose to add or subtract is entirely your choice. You can still tell they're all disgusted in different ways (unimpressed, grossed out, and annoyed) by their expressions before I lay it on real thick. To get better at identifying the general shape of the most important facial features, try tracing photos of people pulling very easily read expressions. Even if you're going for subtly, it helps to start with exaggeration beforehand because then you know what you can tone down and what is important for the expression to be read.
Pushing the expression after you understand it can be extremely useful, whether you're doing realistic work or more stylized stuff. When I'm sketching, I tend to push and push the drawing as I go along before I settle on something I like. Sometimes I do it less, sometimes I do it more. If you wanna take the same approach, you might find it useful. Dig deep down in your brain and try and scrape up what you know about an expression already: when someone's sad, they may cry. Their eyes and nose scrunch up, their frown is intensified, they may be overcome with emotion, mucus may be involved, etc. Combine that with reference material for the best results.

Part 1: http://www.furaffinity.net/view/25971580/
Part 2: http://www.furaffinity.net/view/25971612/
Part 4: http://www.furaffinity.net/view/25971675/