If you really want to be an artist and work on PC, you should take a graphics tablet. Drawing with the mouse on PC is really a pain even when you are a good artist. Wacom is well known for that and they have a tablet for beginners : the "Bamboo" model. Don't take a huge one. I took one and I only use a small portion of it.
Of course, as it has been said you can also draw on paper and scan the drawing to color it.
If you think Mathematics for 3D Game Programming and Computer Graphics is too advanced for you, (or at least too fast on the basic) you should take Practical Linear Algebra: A Geometry Toolbox.
The first half is about linear algebra in 2D and the other half about 3D and some pages about the curves. It's a pretty good book and it will give you an intuitive look about linear algebra with practical explanation of the maths and drawings, rather than an approach with proofs and theorems.
Also please note that there are many different ways to implement this solution but the idea stays the same : you create some components which represent behaviors or features and you create your final object by assembling the components you need.
The "easy to learn hard to master" doesn't fit for every game. For me it depends on the game and the audience you want.
For example, if you want to do a shoot'em up, it should be hard, if not really hard like a dondonpachi.
Another example, if you want to do an adventure/action game, it can be easy (Zelda) or hard (Dark souls) and both choices are perfectly fine depending on the audience you want.
(Of course on the business side, it's another matter)
If you want more tutorials/inspirations, you must go on PixelJoint.com. There are a lot of pixelart gurus on this website. http://www.pixeljoint.com/default.asp The tutorials are in the Feature menu.
Pixelizing your drawing as Prinz Eugn suggests is a good way to start. But remember that you must remove some parts if you downscale a lot to have a readable sprite. And here begins the fun part of pixelart : optimization of the pixels to draw what you want with a limited number of pixels