Although it would be much easier to create a Movie Clip of a face and put it on the stage using addChild, we will draw a face here for illustration purposes.
Before you start to write the code, look at this illustration to understand the math:

In the movie below, a small red square with a blue dot in the middle is drawn whenever the user clicks on the stage.
stage.addEventListener(MouseEvent.CLICK,drawFace);
function drawFace(e:MouseEvent) : void {
//to make the calculations easier we will set x and y to stageX and stageY
var x,y:int;
x=e.stageX;
y=e.stageY;
//draw a circle with a black stroke and a yellow fill
this.graphics.lineStyle(1,0x000000); //width of 1, black
this.graphics.beginFill(0xFFFF00); //yellow
this.graphics.drawCircle(x,y,15);
this.graphics.endFill();
//draw the left eye
this.graphics.beginFill(0x000000);
this.graphics.drawCircle(x-5,y-3,3);
this.graphics.endFill();
//draw the right eye
this.graphics.beginFill(0x000000);
this.graphics.drawCircle(x+5,y-3,3);
this.graphics.endFill();
//draw a mouth
this.graphics.lineStyle(2,0xFF0000);
this.graphics.moveTo(x-5,y+6);
this.graphics.curveTo(x,y+10,x+5,y+6);
this.graphics.moveTo(x+5,y+6);
} //drawFace
Download the movie to experiment.
Experiment: Try drawing another shape.