Cut down and remove the Virginia creeper if it is growing amongst wanted plants. Cut it down to the ground with a pair of loppers. If the plant is not growing near other plants, this step is optional.
Spray new sprouts with a non-selective post-emergent herbicide, such as glyphosate. If you did not cut down the vine down first, apply the herbicide to the foliage of the entire plant. Use herbicides on a calm day and away from pets and children. Do not spray on other plants or on tree bark. Read the label for proper use and dilution rates, if applicable.
Respray the Virginia creeper as necessary. Spray new growth when it appears. If you didn't cut down the plant, respray any areas that did not die within a week or two. It will most likely take several herbicide applications to kill the plant completely.