How do I match the smooth texture of a new sheetrock repair to the sandy texture of the old plaster?

 

That sand texture is done by putting sand in with the paint. A real pain to match. Sand comes in different grits so try to get the right one that matches.

 

The most common grit of sand in sand finish plaster is ordinary plaster sand screened through a mesh the size of window screen and mixed with the dry plaster by volume in equal parts. It's hard to match a sand finish that has been painted a few times. I think you get a better match by putting sand in joint compound and floating it with a red sponge float. I've done acres of this.
Timing of the floating is crucial and I don't know how to tell you when it is ready. If it is too wet you will know it and if it is too dry it's too late.Whe it's jsut right it's quick, easy and beautiful. You can also feather the new sanded joint compound onto the painted plaster, something that you shouldn't do with plaster on painted plaster.