Check the vine you are going to cut and replant for signs of dehydration, malnutrition or damage. Vines that are wilted, discolored, physically damaged or suffering from insect infestation are less likely to produce a new vine.
Combine peat moss and perlite in equal measures, and mix them thoroughly until you have enough potting mix to fill your plant pot. Clean your plant pot with soap and water, then wipe it down with rubbing alcohol and allow it to air dry. Wipe your knife with rubbing alcohol and allow it to air dry.
Look for a section near the vine's tip that is free from damage. Measure off a 6- to 8-inch section that contains at least one leaf, and sever it with your knife. Make a clean cut, and avoid crushing or stripping the vine or the cutting.
Pour a small amount of rooting hormone into a plastic bag immediately after the vine is cut. Make 1-inch long incisions up the stem on opposite sides of your cutting near the severed end with your knife.
Dip the cuttings' severed end in the rooting hormone until the cuts you made are covered. Shake the stem gently to dislodge excess rooting hormone clinging to the stem. Remove all but two leaves from your vine to help prevent it from dehydrating.
Make a hole in the center of the potting mix with your finger that is 3 to 4 inches deep. Put the severed end of the vine into the hole, and fill it in with loosely packed dirt.
Water the soil immediately around the cutting lightly, then place a clear plastic bag over the pot and secure it tightly. Move the pot to an indoor area out of direct sunlight. Remove the bag and lightly water the base of the vine cutting often enough to prevent the soil from drying out, but avoid saturating it with water.
Keep your vine out of direct sunlight, and moisten the soil often enough to prevent it from drying out until the vine establishes new roots. Keep the clear plastic bag over your pot until the vine has begun to form new roots. Depending on the growth habit of the species you are propagating, it can take up to 12 weeks for your vine to produce a new root system.
Gently tug on your cutting once a week to check for new roots, but do not remove the cutting from the soil. You can tell that new roots are forming when the vine resists pulling out of the ground. Use your knife to perforate the plastic bag once the vine begins to root.
Wait two to three weeks for your vine to establish several roots that are at least 1/2 of an inch long. Fill a plant pot that is at least 4 inches in diameter with topsoil and transplant your vine into it. Take care not to damage the new roots of the vine.