Wow, a topic I might be able to answer some, seeing how I've been drawing my entire life (despite this there's scant evidence of it online, given that I tend to not scan my results -- I'm a very analog artist... that, and I dislike showing what I consider failures... although I suppose it would be useful for some?).
Victor's answer addresses the first thing: hand drawing. Kimon Nicolaïdes is probably one of my greatest inspirations, and I'm sad that I never got the chance to study under him.
"There is only one right way to learn to draw and that is a perfectly natural way. It has nothing to do with artifice or technique. It has nothing to do with aesthetics or conception. It has only to do with the act of correct observation, and by that I mean a physical contact with all sorts of objects through all the senses. If a student misses this step and does not practice it for at least his first five years, he has wasted most of his time and must necessarily go back and begin all over again."
It might sound extreme, but at the time (around 1936) it was a rather common idea (Harold Speed says something similar about practice); compared to today's idea that some people have a natural talent and the rest of us can never catch up, they believed that practice, practice and practice will get you there -- maybe a bit later, but eventually.
Personally, I don't believe in talent. Not in the way media plays it up these days. See, what everyone forgets is that even talented people practice, and there's even evidence that "special talent" doesn't really exist. (Which is good news for us mortals.)
Kimon Nicolaïdes's book, "The Natural Way to Draw", is great, and I regularly re-read it and go through the study plan. Another great book is Harold Speed's "The Practice & Science of Drawing"; although it lacks a proper study plan it will give you several points of view on drawing and painting.
But, back to the topic at hand. As Victor said; you will want to practice hand drawing, because it will force you to learn perspective, shadows, textures and similar. Indeed, I don't think you should concern yourself overly much with the digital part yet (actually, I wouldn't be able to say since you've not said nor shown at what level you're at except "simple drawing", which is vague enough to not mean anything :P ); what you're training would be the base for everything else, and without a proper foundation you won't get very high. A quick word of advice: don't throw away your sketches/drawings. Save them -- at least for a few years; whenever you feel like you're not making progress, look at your first ones and you'll be astounded at what a distance you've come.
Hand drawing (and by this I mean with any media: charcoal, graphite, pastels, conté, silverpoint, pen and ink, marker, what have you) will probably be enough for pretty much everything except sprites (sprites could probably be made either by hand or by doing some fancy magic with 3d models -- it's not an area I will claim any expertise). Backgrounds can be made in any media, but watercolours are nice and very rewarding once you've learned them. I remember a few (10-15) years back when I asked a friend of mine how she did her amazing watercolour paintings... Because I'd never been able to produce anything like it; the answer was simple enough: practice, and letting the painting dry before continuing with the next part of it. Not getting the brush wet enough, or getting it too wet -- those parts were just part of the learning curve.
Once you're comfortable with hand drawing and painting/backgrounds, you're pretty much done with the analog part. Learning the software necessary for digitizing it is another step altogether, and one where the same thing repeats itself: practice, practice, practice. Find a good book or two dealing with your software of choice, and start learning (lynda.com has some great video tutorials for photoshop). It's less work, in my opinion, to learn how to digitize something -- software is just a tool, just like your silverpoint or graphite. It's a means to an end, it's not the end result itself. One thing though: when you start using software, get a pen tablet. The ipad and its ilk are horrible at the job, but wacom's intuos, cintiq or even bamboo pen&touch will be worth their weight in gold when it comes to digitizing or any job in photoshop. Mouse and keyboard are great input methods for a lot of things, but not drawing (besides, the pressure sensitivity alone is necessary for a majority of operations).
Alex Shepard's advise, "practice like crazy" is true. His way is one way, another is the way I learned it way back when: pick a subject -- easier things when you're starting out, then draw it for 30 minutes, without looking at your sketchpad. If you feel that you're losing the connection between subject and paper, take a second to glance at your sketch/drawing and reposition the pen. Because drawing is being able to draw what you see, not what you know is there.
Before people jump down my throat on the "it's less work to learn how to digitize something"; I realize that it might sound a bit arrogant. Learning the magic that photoshop can do requires a lot of practice and effort, and don't even get me started on 3D modelling because that's just way out there. But learning to use it passably is a lot easier than learning how to draw a person without it looking like it's from some forgotten horror show. In my opinion.