I already found this question, but it only talks about the kind of software used - not the actual methods. Were they drawn at a high resolution first and then shrunk down? Or did you just zoom way in? Do you do a vague outline first, then make it more detailed? How was the coloring done? And when you have to do long animations, do you hand draw each frame, or are there tools to help automate the process? Or do you just copy paste the basic sprite and only change the moving parts?
Etc.
Pixel art is its very own art form. There are several tutorials on the net about it, but basically you plot one pixel at a time.
Here's a few tutorials, but I'm sure you can google for more:
There are some tools for sprite animation creation, but those are relatively recent; back then people just drew the animation frames with deluxe paint (or similar).
Gas13 has some guides to drawing classic pixel art written down. These are really general theory stuff- he's not going to hold you by the hand in step-by-step tutorials, but instead explain the principles on what makes a good game sprite.
I would start with this following page:
http://gas13.ru/v3/tutorials/sywtbapa_almighty_grass_tile.php
Even something as mundane as creating a grass tile can be improved in detail, and then you can learn how to move on draw more complex objects with depth and definition, using a limited color palette.
