Edit in JSFiddle

// grab the canvas element, get the context for API access and 
// preset some variables
var canvas = document.querySelector( 'canvas' ),
    c = canvas.getContext( '2d' ),
    mouseX = 0,
    mouseY = 0,
    width = 300,
    height = 300;

// resize the canvas
canvas.width = width;
canvas.height = height;

function draw() {
  // set the colour
  c.fillStyle = 'lime'; 
  // start a path and paint a circle of 20 pixels at the mouse position
  c.beginPath();
  c.arc( mouseX, mouseY, 20 , 0, Math.PI*2, true );
  c.closePath();
  c.fill();
}

// get the mouse position on the canvas (some browser trickery involved)
canvas.addEventListener( 'mousemove', function( event ) {
  if( event.offsetX ){
    mouseX = event.offsetX;
    mouseY = event.offsetY;
  } else {
    mouseX = event.pageX - event.target.offsetLeft;
    mouseY = event.pageY - event.target.offsetTop;
  }
  // call the draw function
  draw();
}, false );

<canvas></canvas>

*{margin:0;padding:0;}
canvas{background:#69c;}