First of all, you should purchase the cultured marble pieces which are easily available at all home improvements stores in town.
You should measure the wall where you want to install cultured marble wainscoting and make sure that you have marked it with a straight line on the wall from one corner to the other.
Now, place the piece of cultured marble against the wall in order to check its height and do the same with all pieces making sure that they are equal in size.
Use a jigsaw for cutting the marble into required sized pieces. You should start with a small cut and make sure that you reduce the vibration to maximum possible limit which will help you in making a clean cut.
Now you should use adhesive material to the marble after cutting the cultured marble into required sized pieces. Apply adhesive material to the back of the cultured marble. Make sure that you have covered all area fully.
Then place the piece touching against the wall and press it until it gets fixed with the wall by the help of adhesive material. Keep pressing it until it gets fully attached with the wall and then take off your hands. Follow the same procedure for all other pieces of cultured marble.