Load the caulking gun with your chosen adhesive. Cut the tip of the tube of adhesive off with a utility knife. Leave at least a 1/4-inch-wide hole in the tip.
Apply adhesive to the bottom sides of the first layer of stone to go down, as well as on their sides where the pieces meet up together. Squeeze the adhesive out of the caulking tube tip slowly, and apply an even seam of adhesive with the tip. For stone, keep the adhesive on the back edge of the sides only.
Ensure the adhesive is at least 1 inch away from the face of the material on stacked blocks and bricks, to avoid excess squeezing out and becoming visible through the front joints.
Tap the pieces into place against one another with the rubber mallet. Use the level to ensure the face of the installation is plumb from side to side as well as up and down. Wipe up any excess adhesive that squeezes out by accident with a spare towel.
Work your way up the wall until you are finished, stacking the stones as you would normally, and adding glue to them. Alternate rows so the vertical seams never line up.