Smoothing vertices of a polygon

I would like to smoothen the vertices of polygon. How could that be done? I just want to avoid sharp edges? Please give me some suggestions.

    Each vertex must have a normal.  If your surface comes from a modeling program
    it may have vertex normals already computed for you.  Otherwise you'll have to
    compute them by averaging the polygon normals sharing each vertex. Then, before
    drawing a vertex, call glNormal (.....).  That's all there is to it. You must also turn
    smooth shading on using the command below...

        glShadeModel (GL_SMOOTH);

Note: These comments apply to Fixed Pipeline GL.

Actually I wanted to say that I have a contour (boundary) which is a connected set of vertices. It looks a bit rugged. I want to make it look a bit smooth keeping the number of vertices same, but vertex coordinates may be manipulated. How can that be done?