This technique is a rather simple one, which requires you to carve into the layer(s) of wax by dragging or pushing with a tool. Exposing the layer(s) underneath can easily be achieved by remove only the layer(s) you wish; this takes practice and may require a thick under layer of encaustic. Different tools offer different results: for example a burnisher pushes the paint aside, creating ridges (known as burs in dry point) along the edges of the cup shaped incision; if there are under layers, they will be highly evident- rather than using a straight gouge. On the other hand, the burs can be beneficial by acting as a dam, holding back liquid wax from spilling into another section; this technique takes lots of practice and can be a challenge even for experts.
Screen-printing or Silk screening is really no different from the method used in printmaking, except that you are printing on the encaustic surface instead of paper or cloth. Remember when employing this method to use a compatible ink or paint, some inks may affect the binding properties of the wax if they are fused between layers; if you are not sure, make a practice sample. If you plan to print on the surface of the wax when the encaustic is finished, it is best to fuse the surface lightly.