A very simple example of using multi-touch on Android to build a custom View for finger painting. This example uses the Path class from the android.graphics package. Feel free to use this code as you wish for your own multi-touch apps.

PaintView.java

public class PaintView extends View {
    public static final int MAX_FINGERS = 5;
    private Path[] mFingerPaths = new Path[MAX_FINGERS];
    private Paint mFingerPaint;
    private ArrayList<Path> mCompletedPaths;
    private RectF mPathBounds = new RectF();

    public PaintView(Context context) {
        super(context);
    }

    public PaintView(Context context, AttributeSet attrs) {
        super(context, attrs);
    }

    public PaintView(Context context, AttributeSet attrs, int defStyle) {
        super(context, attrs, defStyle);
    }

    @Override
    protected void onAttachedToWindow() {
        super.onAttachedToWindow();
        mCompletedPaths = new ArrayList<Path>();
        mFingerPaint = new Paint();
        mFingerPaint.setAntiAlias(true);
        mFingerPaint.setColor(Color.BLACK);
        mFingerPaint.setStyle(Paint.Style.STROKE);
        mFingerPaint.setStrokeWidth(6);
        mFingerPaint.setStrokeCap(Paint.Cap.BUTT);
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);

        for (Path completedPath : mCompletedPaths) {
            canvas.drawPath(completedPath, mFingerPaint);
        }

        for (Path fingerPath : mFingerPaths) {
            if (fingerPath != null) {
                canvas.drawPath(fingerPath, mFingerPaint);
            }
        }
    }

    @Override
    public boolean onTouchEvent(MotionEvent event) {
        int pointerCount = event.getPointerCount();
        int cappedPointerCount = pointerCount > MAX_FINGERS ? MAX_FINGERS : pointerCount;
        int actionIndex = event.getActionIndex();
        int action = event.getActionMasked();
        int id = event.getPointerId(actionIndex);

        if ((action == MotionEvent.ACTION_DOWN || action == MotionEvent.ACTION_POINTER_DOWN) && id < MAX_FINGERS) {
            mFingerPaths[id] = new Path();
            mFingerPaths[id].moveTo(event.getX(actionIndex), event.getY(actionIndex));
        } else if ((action == MotionEvent.ACTION_POINTER_UP || action == MotionEvent.ACTION_UP) && id < MAX_FINGERS) {
            mFingerPaths[id].setLastPoint(event.getX(actionIndex), event.getY(actionIndex));
            mCompletedPaths.add(mFingerPaths[id]);
            mFingerPaths[id].computeBounds(mPathBounds, true);
            invalidate((int) mPathBounds.left, (int) mPathBounds.top,
                    (int) mPathBounds.right, (int) mPathBounds.bottom);
            mFingerPaths[id] = null;
        }

        for(int i = 0; i < cappedPointerCount; i++) {
            if(mFingerPaths[i] != null) {
                int index = event.findPointerIndex(i);
                mFingerPaths[i].lineTo(event.getX(index), event.getY(index));
                mFingerPaths[i].computeBounds(mPathBounds, true);
                invalidate((int) mPathBounds.left, (int) mPathBounds.top,
                        (int) mPathBounds.right, (int) mPathBounds.bottom);
            }
        }

        return true;
    }
}

You are correct. initGrid is supposed to be called inside of onCreate, like you wrote. If you want to empty the grid (to start the game again), you can call initGrid again. setGridTile can then be called in your onTouchEvent-method, where you pass the ID of the finger (or color) and the position.

If i want to draw a circle graphic by using canvas.drawCircle
how can I do