Select the right vine. You want a vine that is right for the climate zone you live in, the climbing surface you are providing, and the sun exposure the vine will receive. Twining vines wind around their support system. Vines with tendrils or hooks will attach to rough surfaces or open fences by themselves. Some vines, like ivy, have aerial rootlets that grow into a masonry surface. These vines can damage stucco, brick or block mortar. Other types of vines need to be physically attached to the climbing surface with plant ties. Keep in mind the chore of pruning every spring before you purchase a vine. Picking a hardy evergreen vine will require less maintenance.
Select the support system. Vines need something to grow on or they will act like ground cover. If there is nothing for them to climb, such as a fence or wall, you can use a trellis or arbor. Choose a material for the trellis or arbor that can handle desert sun and dry air. Wood will be a constant maintenance headache, especially once it is covered with vines. Wrought iron or metal are the best choices.
Dig the hole no deeper than the height of the root ball, and three to five times the width, sloping the sides. Carefully remove the plant from the container, and set the plant into the hole. Tease the roots away from the root ball to encourage lateral growth. Backfill the hole with native soil. Do not fertilize; do not add soil amendments. Tamp the soil, and water it well. Apply mulch or compost on the soil surface to conserve moisture.
Water the plant daily for one week, every other day the next week, and every two days the week after, until you are watering twice a week in the summer, or once a week in the winter for the first two years. Depending on the drought adaptation of the variety, you may be able to water less often after the vine is mature. Check with a reputable plant nursery if you are not sure. As the plant grows, direct it where you want it to grow, or use plant ties.