Generally, plan out motions with simple shapes and work the details out later.
This is especially true for tiny characters.
Simply copying and moving/rotating parts (like for instance the head in fighter sprites, it almost always looks the same) around is also a very good way to save time but that only really becomes possible with larger sprites.
Knowing the basics of animation like how a generic walk looks, anticipation frames etc. will greatly help you to make convincing animations.
And last but not least, unfortunately there never really is a "fast way" to do this, this is especially true for explosions which need to be drawn from scratch each frame.
Animating is nothing but work. You will need a lot of patience.
As for how to plan motion, for me, it's usually a guesstimation of the basic movement followed by a lot of polishing.
I'd suggest reading the
animators survival kit.
It covers planning out walking animations in depth and walks are pretty much the hardest thing to animate right.
Also last but not least, take a look at
this.Intimidating, isn't it? How on earth could anyone get something like that done?
The answer to that is actually quite simple, don't animate everything at once.
Do it step by step.
Take a look at the
WIP stages to see what I mean.
The same applies to every other animation too, for example if your character has a tail, get the walking down first and then do the tail movement.
Big motions first, small motions later so it all comes together.
You simply won't be able to animate everything at once.
Sounds like common sense but it makes all the difference.