I didn't used to be able to draw, until this summer, I learnt so frigging much about drawing in my summer course. Being taught a lot of the theory behind drawing was tremendously helpful to me, and in combination with that, and having a teacher to nudge me along and point out things I didn't realise I was doing badly, I learnt a pretty crazy amount about drawing for someone who had never really done it before. It's... pretty hard to just describe it without being able to show it to you, but I think I can provide some good advice.
There's several things it's important to understand.
First of all there's many different styles and methods behind art, even just within the context of drawing with a pencil. There's more photorealistic styles, and there's more impressionistic styles. But in all cases it's important to understand that art is all about creating an illusion.
Say you're looking at a tree through a window, you see it's greens and it's browns and all it's shades. Then where you see these colours on the window you paint them, and you do it so finely that when you're looking at it from the right perspective, you can't tell the drawing is even there. Now imagine the tree doesn't even exist.
This is what you're generally trying to accomplish with drawing, you're trying to create the illusion of something being beyond the paper. Now there's much more realistic illusions, and much more simplistic illusions, but it's not necessarily a bad drawing if it doesn't reflect reality very well. You would not consider a typical comic to be a realistic drawing, but it's honestly not supposed to be.
Secondly, I recommend learning to draw by drawing from real life, it doesn't have to be portraits of people, objects work too, though I found my self portrait to be very enlightening (though at first I hated it). You can also do it based off of photographs or such if you want to draw something you don't have readily available, but I think I recommend this less, you can't really move around and get a feel for the dimensions in the same way.
I also really don't recommend trying to draw imagined things at first. Fact is you probably don't understand the way things are structurally, and how to draw them nearly well enough to pull this off, and you'll just wind up getting frustrated because it still doesn't look right and you don't know why. You should probably leave that sort of thing off until you have a good grasp of the real world. The one exception for this is probably perspective drawings, they drove everyone else in my class nuts, but I loved them, and could do them very naturally (because I have a good head for spaces), I suspect given your background and personality you'll be the same.
The third bit of advice I have is simple. Don't worry too much about ruining your drawings, you learn the most when you're doing things wrong. Every failure is a potential success if you take the time to learn from it.
Be patient, it often takes a long time to do a good drawing, even if you're very good at it.
Also keep in mind there's a hell of a lot of ways to draw things, and a lot of different styles. All typically arranged on a scale from "realistic" to "impressionistic".
I think I'll post a picture of my perspective drawing of a church, and tell you a bit about it, hopefully sometime tomorrow I think.