Purchase a tomato plant that is at least 8 inches tall with a hearty stem. The grafting process can be hard on plants, so they need to be healthy to survive the process. Purchase a healthy potato plant as well.
Remove the plants from their pots. Stand them next to each other so the two stems are almost touching.
Cut a thin strip about two inches long down the side of the potato plant stem. Do the same for the tomato plant (at the same height).
Pull the plant stems together so that the cut areas are in direct contact with each other. Secure them in place with grafting tape. Make sure that all of the cut surface is covered so that there is no chance for disease to enter the wound.
Place the new grafted plant in a large pot, and water it thoroughly. Keep it moist for the next two to three days.
Watch the plant for the next week. If you see a bulging of the area that has been taped with grafting tape, then the graft has been successful. Wait about one more week before pruning the plant.
Cut off the top of the potato plant just above the graft. Seal the top of the cut with super glue. Cut the stem of the tomato plant as well, this time just below the graft site. Remove the stem from the pot, and toss it aside. Super glue this cut as well.