How can I paint Antique Furniture?

I'm assuming you mean dresser and not dress. I am an advocate of never stripping or painting an antique piece of furniture. However, in your case, it seems the piece has already been painted black. In that case, I would consider the type of wood....if it's a quality wood....walnut, cherry, etc., then I would strip it, seal it and leave it natural wood. If you just want a different color, and the paint isn't peeling, chipping, etc., then you might just give it a light overall sanding, then paint the color you want.

I agree with the above, stripping and trying to preserve the piece. However, if you need to paint it, chalk paint requires no prep work. You just clean and paint. No sanding or primer needed, and you could even distress it to add to the antique look of it.

use kilz paint in the color you plan to use. lightly sand and paint

You can use Chalk Paint directly over the currently painted finish. Have fun with your project!