The particular way each vine climbs determines what sort of support you'll need to provide.
As these vines grow, their stems twist and spiral. They coil too tightly to grasp large supports such as posts, so give them something slender, such as cord or wire.
To cover a wood fence with chocolate vine (Akebia quinata), for example, string wire up and down the fence through eyescrews attached at 6- to 8-inch intervals. Twining vines with moderate growth habits are also good choices for growing on fan-shaped or rectangular trellises with narrow vertical members.
If you want a twining vine to spill over the top of an arbor, you can sink a narrow pole into the ground beside the structure and train the vine around the pole; when it reaches the top, it will twine along horizontally, with streamers of stems and leaves trailing downward.
Besides Carolina jessamine, twiners include include Dutchman's pipe (Aristolochia macrophylla), honeysuckle (Lonicera), and wisteria.
Vines with tendrils or coiling leafstalks
Tendrils are specialized plant parts growing from the end of a leaf or the side of a stem. They grow straight until they contact something they can grasp--wire or cord, another stem on the same vine, another plant--then reflexively contract into a spiral and wrap around the support. Vines that climb by tendrils include grape and sweet pea (Lathyrus odoratus).
Some plants (clematis is the best-known example) ascend by coiling leafstalks: as a stem grows and puts out foliage, the leafstalks of young leaves encircle anything slender they encounter, behaving more or less like tendrils.
Like twiners, vines that attach by tendrils or coiling leafstalks need slender supports; if the support is too thick, the vine will merely attach to its own stems, growing into a tangled mess. These vines are excellent choices for latticework supports such as chain-link fences and lath trellises.