How to even begin?
If you're unfamiliar with the very basics of modding Starbound, I'd highly recommend familiarizing yourself with them first, by starting here[community.playstarbound.com].

What software to use?
Doesn't really matter, as long as it's something you're comfortable with.
Other modders often recommend PaintNET[www.getpaint.net], Aseprite or Piskel[www.piskelapp.com]
I personally use Photoshop (since it's what I'm most familiar with), which is probably not the best thing to use for pixel art - so unless you already know it well, I'd recommend against it.

Many in this community seem to be struggling with this aspect, and are often discouraged by how complex it seems at first glance, when in reality - it is anything but. Animating Starbound's tiny pixel art is something anybody can master with just a little bit of patience.

This way of animating makes creating simple animations even simpler by breaking them down into easy-to-follow steps, and is something that was vaguely described to me a while ago by a person who does this for a living. There are many other tricks and ways of doing this, but I found this one to be the easiest and most convenient for the things I make.

I'll use a floofy tail run animation from my Neki mod as an example.

• Start with a basic, 1-pixel-wide line, roughly representing your "cloth":
  
  
• Create a few additional lines and tweak them till they start resembling an animation; this is probably the step that requires the most patience:
  
  
• Test your animation for smoothness; it doesn't have to be perfect yet:
  
  
• Expand upon the line you've created or complete an outline of the the object, like so:
  
  
• Keep testing and correcting your animation:
  
  
• Fill the empty spaces and test some more, this will make errors easier to spot:
  
  
• Once you're satisfied with the basic animation, add detail and shading:
  
  
• Repeat the process for any additional animations as required. Use the frames you've already created as a reference and a baseline, and don't be afraid to outright re-use some of them altogether for different animations. This can save a lot of time :)

Keep at it, test the animations in-game and play around with it. A few hours, days (or weeks, in my case T_T) later, you'll hopefully end up with a set of animations that you're satisfied with and ready to present to the world.

I hope this guide helps those struggling to even begin animating things for their mod(s). If you have any ideas on how to improve this guide or even better ways to animate that you've mastered - please share!

- Juni ♥