In a shallow pot or using peat pellets, plant your tomato seeds according to package instructions. Keep the soil consistently moist and wait for seedlings to sprout. This should take about a week.
Fill a large pot or container with potting soil, and plant a cut part of a white potato that has several eyes (sprouts). Water immediately after planting and wait for sprouts. This should take about 2 weeks.
Once both plants are 8-10 inches high, you can start to graft them.
Using a sharp knife, carefully cut into the tomato stem, where you are planning on making your graft. Only cut a very thin sliver, which should be no more than 1/3 the thickness of the stock. When cutting, be careful not to cut through the tomato stem – you're basically just making a very thin slice.
Repeat this process with the potato rootstock. Be careful with your potato plant as well to not cut through the stem, but only slice.
Bend the two cut stocks very gently and combine them together so that they touch as closely as possible. See image above.
Once the cuts match, wrap the cut stems with grafting tape. If you don't have grafting tape, you can also use plastic wrap. Make sure that the stems are secured and in place.
Move the plants away from sunlight and ensure that the soil is moist.
Now, keep an eye out for new growth on the top of the tomato plant. There should also be a slight bulging on the side of the graft.
Once it has completely healed, cut away the part of the potato above the graft site.
In about 2-3 weeks, once the tomato shows signs of growth, cut away the part of the tomato plant below the graft.
Cover the plant in a clear plastic bag for several days to give moisture. If the plant looks wilted when you remove the bag, leave the bag on for a few more days.
Watch your plant again for new growth. Once you see this, you can go ahead and remove the grafting tape or plastic wrap.
Remove any new growth from the potato rootstock as it grows. If you don't do this, the potato plant will outgrow the tomato plant.