The one thing I can say had the LARGEST weight on how nice my pixel art looked was not WHAT I learned. It was HOW I learned. With many things, pixel art in particular, you will start out with little to nothing and the more you learn, the better you get. But if you get better at learning, which can take time to develop the patience for, then you will exponentially get better at pixel art.
So, if you really do have a passion to LEARN how to do decent pixel art, then listen carefully. I don't want you to skip any part of this. Another thing I have found when developing as a pixel artist is that EVERYTHING I SKIPPED, SKIMMED, OR NEGLECTED ended up making HUGE CHANGES in my art quality when I did implement them. Things like color theory, anti-aliasing, line form... among many, many other things... I would just skip over! I wasn't learning ANYTHING to start. That's the one thing I regret most about my career as a pixel artist, is that if I had the patience to really take in the information I read from various tutorials, then I would have actually become A LOT BETTER, A LOT FASTER.
Okay, enough ranting about learning. I hope you get the message there.
So, by definition pixel art is of course art, using pixels. If you understand your basic art principles, and can apply them, then you're already a far leap ahead of the rest. I've discovered that the better I get at doing things like pencil sketches, the better I am with pixel art.
When you're doing pixel art, or any art for that matter, always make sure you're constantly THINKING. Think to yourself, "Hmm, my light source is coming from there, so that edge should have a highlight... Hmm, I'm going to make my shadows nice and saturated, and then go down in saturation as I increase the brightness... Hmm, the perspective on this shape should shift a bit that way when the creature walks.." LOTS of thinking. You have to carefully analyze your artwork as you do it.
This isn't a lesson in the basic art principles, but when I do come across them I will take my time to explain them. They are VERY important and ABSOLUTELY NOT JUST BITS OF INFORMATION! The art principles are the THINGS YOU THINK ABOUT WHEN YOU'RE THINKING. Like I said, don't just LEARN them, make sure you can APPLY them in an effective way! This can take practice, or hardly any practice if you're a good learner!
Pixels! They are charming little squares of color that fill countless monitors across the world with life. As a pixel artist and game developer, it is my job to use these pixels to bring life to my own creations.
What makes pixel art different from, say, painting? Well, the pixel part! You have to manipulate the way that the tiny pixels form an image and trick the eye by "blending" next to their neighbors, while still using as few colors as you can.
So let's get to the pixel art, starting with a concept. Before I draw anything, I need a concept to get myself going. A clear image of the thing I'm about to draw in my head, or if it is not my own original creation or if I'm basing it off something else then I'll put out google and find a reference. The concept here is going to be a little cube-shaped robot with little claws which it uses to scuttle around. First, I draw an isometric cube. It's meant for top-down perspective, but I think to myself, "Hmm, a walking cube in top-down isn't going to be nearly as interesting as a walking cube in isometric." Part of the thinking process!

When the cube was drawn, I trimmed down the edges so that it looked a bit rounded on the sides and went inward at the bottom. This is for the sake of style. A normal cube is rather boring to look at, as opposed to a nice round cube. Now, since this is lineart, I'll discuss what NOT to do when drawing lines, and how to fix it.
This picture sums it up.

STUDY THAT CLOSELY! And APPLY IT! I recommend that you try drawing something of your own that you know the definite shape of while you read this and apply the things I demonstrate! Don't try drawing something you aren't sure of, though, like a human -- Do something simple, like a vase!
Now that we have the basic shape for our little robot, let's color him up! I want this to be plasticky and stylized to be a bit cartoonish. ALWAYS think of style when you're doing art! At first, stylized art will be VERY difficult to do, but the more experience you get, the more control you will have over what style your piece has. So let's color him! I'm selecting some unsaturated grays, and using white as his highlight. Gray can look saturated, or not saturated at all, depending on how you use it.

There! We're now done. Your sprites won't always be metal and plasticky, though. Every material reflects light differently, and the only way you can get better at showing this is by studying the artwork of others and practicing for yourself. Personally, I had to study the metal textures drawn by Zane444 in order to get a firm understanding of how I should shade the shape. I took about 10 minutes to study his most recent blog, and carefully looked at how each material received light. And then I applied what I learned as fast as I could before I forgot it, so that it's now stuck in my head. I'm a good learner, and I get exponentially better at art when I study it because of that.
Like I said, not every texture you'll be making as a pixel artist is smooth and plasticky. Now I'm going to discuss two things: Anti-aliasing and dithering. THESE ARE MUST-LEARNS, and WILL MAKE YOUR PIXEL ART LOOK NICER.
First, I'll explain dithering.

Dithering is important, and if you decided to skip/skim over that, then I confidently say that you will be missing out on a HUGE part of pixel art.
Next, anti-aliasing.

And that's it for today. Remember: If you're a good learner, then you're a great artist. I recommend going and applying what you've learned, asap, before you forget it! The faster you apply your knowledge after learning it, the more instinctual it will be!