Set the starting paths.
Draw two sets of lines along the top and left sides of the shape as shown here. To start, choose the Pen tool, set the fill color to none, choose a stroke color, and set the stroke weight in the options bar at the top. Then click to start the line, click and drag to create a curve, and click where the line should end. Press the Escape key to finish the line.
To taper the end of each line, choose the Width tool, select the point at the end of a line, and drag down to decrease the width of the stroke.