-Can the sketch be drawn directly on a tablet, or does I have to draw on paper and then scan it?
You can... but it won't come out well. It's a last resort when you don't have a scanner or camera. If you can't sketch onscreen (it's okay, many people never manage it) than scanning it or taking a picture is the best option.
-Where can I find a nice introduction to digital art/sketching on a tablet?
I actually don't know. I have a tutorial on photoshop, but not tablets. If you search youtube though you should find some. Mostly you'll get tips on how to set up shortcuts, buttons, and pen settings in photoshop. You might want to search for beginner tablet exercises too.
-How long did it take to get used to a tablet?
I had been drawing on Tablet PCs (directly on the screen) for a few years. I bought an Intuos 5 and was super afraid I wouldn't get used to it (I had tried a friends previously and could not do the hand eye coordination), but in about a week I was used to it. It might take you longer. What I did was just draw circles over and over and over again until they were as good as the ones I could do with a pencil. Then I moved to straight lines. Than to quick sketches. These are the tablet exercises I was referring to.
If you're having wobbly lines I recommend trying broader strokes. Don't attempt slow lines (were you pressed the tip into the paper). I don't know about you but this is a common mistake with cartoonists who do very clean lineart on paper with slow thick strokes. Try using your whole arm more. For places where you need smaller strokes try quick flicks. They should start pointy, get thicker, and end pointy (less pressure, more pressure, less pressure). This might be a bit hard at first but it will allow you to do clean lineart even in Photoshop. The point ends "connect". You usually can't do a line in one go unless you have a program like SAI (with line stabilization).
Just keep practicing. Tablets are not as intuitive as they seem, and it takes a little time to develop the hand eye coordination and muscle memory that you need. But if you just keep at it, it will be second nature before you know it.