In this example the hole hasn't gone back to brick so we can patch the white set with some topping compound. If it did go all the way back to brick we would need to put a cement mix in there, let that dry, then cover it over with the topping compound. To prepare the area rough up the surface using a sanding block and remove any excess dust with a paintbrush.
Mix up the topping compound until it is like thick toothpaste. Apply it to the wall using the hawk and spatula. Put it on thickly to fill the hole, then scrape it back.
Once the topping compound is dry, sand back the area, in a circular motion, until it is smooth, even and ready for painting.
Use a paintbrush to cover the patch with a sealer. Make sure you wear a respirator mask. Let the sealer dry. The wall is ready for a coat of paint.