Mike, if you have green board, it is probably plaster. Since it is textured, you have to figure out how they did the original texturing. Usually, this is done with a brush similar to a wallpaper brush but there are many different techniques to add, remove or texture plaster with a brush.
Normally, the total plaster thickness is about 3/8". For this thickness, you have to build up in a couple of layers. If yours is less and the area is small, you may be able to get away with one layer. Start by misting the area with water in a spray bottle then apply and trowel the plaster smooth. Finally, apply the texture.
You might need to get a piece of greenboard and some plaster and the brush and just play around to see if you can duplicate your present wall. Some textures are applied immediately after the plaster has been smoothed and others are applied after it has set up for a while.