Select a healthy potted potato seedling and a healthy potted tomato seedling that are about the same size. Place them next to each other on a flat surface.
Make a slice in the potato stem about halfway up the length. The cut should be 1 inch long and should remove 1/3 of the stem width. Make an identical cut in the tomato stem at the same height as the cut in the potato stem.
Join the stems together so the cut places are touching. Wrap the cut stem with grafting tape so the cut sides stay touching. Set both plants in a bright spot outside of direct sunlight and keep the potting soil moist. Wait two to three weeks for the graft to heal over.
Remove the grafting tape. Use a razor to cut the tomato plant off below the graft point, and then cut the potato plant off above the graft point. You can then transplant the joined plant to the garden, or keep it indoors in direct sunlight.