Learning how to draw curves is the basis for free flowing shapes, and for good action lines in your keyframes.
In this video, animator Eric Goldberg (whom I first heard of way back, when Aladdin came out), is drawing his Orange Cat character on the Cintiq.
It's all worth watching, but since we're talking about curves here, go to about 4 minutes into the video and see how he draws his curves.
Goldberg draws short arcs, mostly, and uses the zoom function to make the portion of the drawing he's working on comfortable to work on, which is something you can't do with paper.
Do notice that every now and again, when he needs to draw a longer line, he lifts his arm of the screen and draws -you guessed - from his shoulder.
Also, listen to what he says about "Streamlining" at about 5:30 minutes.
Just as with circles - Draw from your shoulder.
A curve is simply a part of a circle, so everything you learned from drawing circles applies to curves.
Make sure your arm swings freely in the air - do not lean or rest it on the table. Practice drawing free flowing curves.
You will find that there is one direction, one angle, that gives you the best result. This is why animators usually turn the paper around when we draw, or use the rotate canvas function (see below). Or rotate the drawing tablet.
Now practice drawing short and round curves, like the letter "C". Draw it in all the directions - curving up, down, to the left and to the right.
Then practice S curves.
Find your rhythm. Drawings go smoothly when you find a speed, a rhythm that works for you.
When animators drew classic animation with pencil and paper, they used a rotating disk that was built into the light table. With a Wacom you can, of course, rotate the drawing tablet (Duhh).
Anyway, Adobe programmers finally realized how handy it is to be able to rotate the canvas itself, so they came up with a "Rotate Page" feature.
In Photoshop it's at the bottom of the Toolbox, together with the Hand tool. (Still not available in Illustrator though):
Press R, Then drag the mouse across the screen to rotate your canvas.
Press Escape, or Double click the Rotate Tool to return to Default.
Missed the How to Draw a Circle tutorial? it's right here