Pour peat-based potting mix into an 8-inch diameter container with a drain hole in the bottom. Make sure the potting soil has perlite, sand or vermiculite mixed into it for good drainage. A good ratio is 1 part perlite, sand or vermiculite to 2 parts peat. Wet the potting mix thoroughly. Stir it with a spoon while wetting it to make sure there are no dry pockets.
Cut a stem section off the Swiss cheese plant with sharp scissors just below a stem or leaf joint. Take at least 2 to 3 inches of actual plant stem, not leaf stem. Make the cut just below an aerial root, if there is one present. Use the scissors to cut the leaves off at the base of the stem. There must be 2 inches of bare stem at the base of the stem cutting.
Coat the cut end of the stem cutting with rooting hormone. Push the end of the cutting into the potting mix at the center of the container. Make sure the bottom 2 inches of stem cutting is pushed into the potting mix.
Use a sharp knife to remove the bottom from a plastic 2-liter soda bottle. Remove the cap from the bottle. Set the bottle on top of the plant carefully to form a terrarium. This keeps the humidity up around the Swiss cheese plant cutting.
Keep the container in a warm location where the temperature will remain above 70 degrees Fahrenheit. Do not place the cutting in direct sunlight. Set it right next to a window that faces south so that it gets bright indirect sunlight. Keep the soil damp at all times.
Take the bottle off of the Swiss cheese plant after it begins to grow vigorously. Allow the top of the potting mix to begin to dry slightly between waterings, but don't let it dry completely. The new roots are very shallow. Place the bottle back on the plant if it begins to wilt and go back to keeping the soil moist. Try removing the bottle again after the plant recovers and begins to grow again.