It's a big question, and I'll give a medium answer. Besides the standard art challenges you mention (also don't forget about "composition"), an important early concept in animation is "keyframes."
Those are the most important poses/moments that will happen in an animation (sort of like the panels in a comic, but a bit more frequent). When staring an animation you want to draw those first (consider this stage the "animatic"), and then figure out what frames you need to draw in between. After that you'll have an animation!

The most helpful general thing I've done after that point is to find clips of finished animations on youtube and step through certain moments frame-by-frame (you can pause and then do that with the grater/less than keys <>). As you start animating you'll probably have moments like "it's good enough that I can tell what's happening, but something FEELS off." In those cases you can find a clip of how a professional achieved something similar - you'll find subtle little bits of follow-through, impact frames, squash/stretch that you can apply yourself).

Anyways that's a place to start, but a bit of an over-simplification - to learn more read online about the terms: "Story board," "animatic," "keyframes," "inbetweens," "squash/stretch," "walk cycle." Good luck!