It's all about ball placement in your stance and your swing. For a fade play the ball closer to your back foot and come over the top a little bit. For a draw, play the ball closer to your front foot and try to come inside the ball a little bit and turn over your wrists. 

FOREWARNING:  There are "old ball fight" laws which are incorrect.  And there are the "new ball flight" laws which are correct.  Know the difference because there are still PGA Pros who are teaching the incorrect, old ball flight laws when teaching how to shape shots.  The old laws have recently been proven to be faulty with the use of devices that use Doppler RADAR technology (TrackMan, GC2, etc.) .

Basically, this is how it works.  There are two major variables (dominating factors) to drawing and fading (hooking and slicing in their extreme forms).  The path of the club head as a whole is one variable.  Then, the other, is the direction the face is looking with respect to the direction the club head is traveling. 

So, if we were to take 60 frames (still pictures) from a video and put a dot on each frame where the club head appeared we would have the club head's path.  It will look somewhat like a curve but for all intents and purposes, we will only be concerned with the few inches before and after the ball.  If we connect the dots that represent where the club head was from each from with a straight line as best we can we would see a path that was either inside-out, outside-in, or square with respect to our target line.

First, we have an imaginary green line that connects the ball to our target.  This is the target line.  With respect to this line, we can have three types of club head paths in a normal golf swing; inside-out, outside-in, and square.  I will not assume you know what these are. For discussion purposes, the golfer stands on the "inside" half of the target line, the club addresses the ball "on the line", and on the other side of the line is the "outside"

CLUB HEAD PATHS (there are 3 club head paths)

OUTSIDE___________________________OUTSIDE

X<-------------target line------- O------------------target line

INSIDE _______________YOU____________INSIDE (feet are standing on this line)

Read the following three definitions.  Keep in mind I am referring to a few inches before and after where the ball is laying when talking about the club head's path.  Think of the club head as just a blob moving.  Don't think about its face when reading these definitions.  The club head is just a metal mass moving on the end of a stick for all intents and purposes in this section.

INSIDE-OUT:  a club head that travels across the line from the inside to the outside.  Before contacting the ball, the club head is traveling from the inside of the target line.  After striking the ball it travels across the line towards the outside.

OUTSIDE-IN:  a club head that travels from the outside line, contacts the ball, and continues towards the inside line.

SQUARE:  the club head travels straight onto the target line, makes contact with the ball, and continues straight down the target line before curving inwards with the natural release of the club head in the follow through.

CLUB FACE ORIENTATIONS w/ RESPECT TO CLUB HEAD PATH - NOT THE TARGET LINE (there are 3 of these too)

Now, pick any club head path from above and you can apply the following face orientations to each one.  Let's pretend their is a light beam emitting from the face and it shines in the direction the face is pointing at any given time.

OPEN:  The light beam on the face would be shining to the right of the club head's path. 

CLOSED:  The light beam emitting from the face would be shining to the left of the club head's path

SQUARE:  The light beam would be shining down the same line the club head would be traveling along.

Again, the arrow is depicting the club head path NOT target line

Now with 3 club head paths and 3 face orientations to combine together (3 x 3) we have 9 different shapes the golf ball can travel: 

I am ASSUMING we hit the ball on the sweet spot (or within a 1/8 inch of it) for the following 9 shot shapes to occur.  NOTE:  If you hit just 1/4" off the sweet spot another phenomenon begins to come into play - the Gear Effect (outside the scope of my discussion).

A. out-to-in w/ closed face:  (HOOK / DUCK HOOK)  You already have the out-to-in path that causes the ball to start left and throw in the closed club face which adds right-to-left spin (hook-spin), and this is the prime recipe for the hook and duck hook.  The closed club face takes loft off the club which is why these shots usually fly lower. You usually hit closed club face shots more solid than the open-faced types so closed-faced shots usually run run run. 

B. out-to-in w/ square face: (PULL) the ball will start left of the target line and keep flying straight in that direction.  How far left is dictated by how many degrees from the outside to the inside the club head is traveling.  1 degree across the line and the ball will barely go left of the target line, 5 degrees across the line and you may be getting into some serious trouble.

C. out-to-In w/ open face: (FADE/SLICE)  Shape = fade to slice; depending on how many degrees the head is coming from the outside to the inside in combination with how many degrees open the face is to the club head's path dictates how much the ball fades/slices.  Due to the glancing blow nature of the open club face, the ball will not travel as far as it normally would and it will fly higher due to the additional loft added by the opening of the face.  Sound familiar, that high flying slice that just keeps getting higher and going further right!  :-)

D. square w/ closed face: (HOOK)

E. square w/ square face: (STRAIGHT)

F. square w/ open face: (SLICE)

G. in-to-out w/ closed face: (DRAW/HOOK)

H. in-to-out w/ square face: (PUSH) just the opposite of #2

I. in-to-out w/ open face:  (PUSH FADE/SLICE).  The club head is traveling towards the outside from the inside which makes the ball start right of the target line.  Combine that with an open club face which imparts the left-to-right spin (slice-spin).

NOW FOR THE DRILLS:  All I can say is learn this information inside and out first.  If you don't understand this post then you will never own your swing.  You will essentially be guessing and hoping.  Also, you will not fade the ball every time you try to.  However, you will now understand what you DID or DIDN'T DO just by watching the flight of the ball.  And when you do go for a lesson, you will totally understand what the instructor is attempting to teach you to swing for right field or... close your stance to the target line, point the face of the club at the target, and swing the club along your toe line which just happens to be how you move the ball right to left (hit a draw/hook).  :-)  Ooops, did I say that?  

"Pretend" there is a circle on the ground.  In the middle of this circle is a golf ball you want to hit.  The circle is of a size where its outline would intersect both of your feet.  Draw a line (or place tees in the ground) that represents the target line (the target line bisects the circle).  Forget about the other half of the circle on the other side of the ball.  You are only concerned with the half that you are standing on.  To hit a DRAW, set the club face down square/perpendicular to the target line.  Now move your feet around the semi-circle clockwise (to the left).  Now make a swing and come down and through along the line formed by connecting your big toes.   The more you move to the left, the more draw (or right to left movement you will get).  Be careful not to manipulate the face back to square or open when making you back-swing or when swinging down.  To hit a FADE, set your club face down square/perpendicular to the target and move to the right (counter-clockwise) on the semi-circle.  Again, swing on a line created by connecting your big toes. 

To add even more DRAW/HOOK, you can place your club face down behind the target line in a slightly closed position. 

To add even more FADE/SLICE, you can place your club face down behind the target line in a slightly open position.

Shawn

I can go into a lot of swing mechanics and diagrams and calculus about tangent lines of circles, but here is my best advise to keep it simple:

For a fade, time your swing to have your shoulders open at impact. For a draw, have them closed.

There has been a fair amount of good information posted to your question, so I'll just say - keep it simple.  You already have a natural tendency to either hit a fade or a draw, so my advice is to primarily stick with that shot shape.  My normal shot shape is a fade and I know exactly what to expect ever time I hit that shot, but I can also hit a draw/hook.  I say draw/hook because I can't control the shot very well.  Take some of the simple suggestions here and try them on the range to see what works.  A word of caution though, if you can't pull the shot off on command on the range, stay away from it on the course.

When I want to draw the ball I'll stand an inch or two further away from the ball than normal.  This promotes a flatter swing plane and an in-to-out path.  To fade I'll stand an inch or two closer to the ball.  Try it next time you're at the range.  YMMV.