It is one of the regular questions, i have been asked many times. If i try to explain it, it creates further confusion.
To help you understand what these three actually mean. I will try to explain it in a simple way.
Drawing : It is a visual art which when completed looks like a two or three dimensional medium. We use instruments such as pencils, pens, ink pens or brushes, color pencils, wax pencils, crayons, charcoals, etc. Drawing are usually made on papers, but other materials like cardboard, plastic, metals, leathers are also used.
Sketching : it is a drawing but it is not considered as a finished work. It is merely a preliminary exploration or sketch.
Painting : It is same as drawing but it is drawn using paints and colors instead of pens and pencils. The medium used to do this painting is mainly a brush. You can find many different kinds of such brushes. Painting are done on walls, canvas, wood, glass, clay, paper etc.
I hope, this clears a little bit.