Plant your jasmine in a well drained container with rich potting soil and place it 6 inches from your trellis to allow for proper airflow.
Thread the young jasmine vine vertically in and out of the trellis's slats. You can keep your plant to one main vine and allow side shoots to spill off that vine. Or you can allow several large vines to grow to create a larger trellis. The shape and size of the vine is up to you. Just help the vines along by threading them through the trellis until they reach the top.
Prune your jasmine after it flowers. Cut out any unwanted vines or shoots. If the plant is growing past the top of the trellis, you may want to trim the top to prevent it from pulling the trellis off the wall.
Water your jasmine when the top inch of the potting mix is dry.
Provide winter protection by either bringing the plant, trellis and all, indoors. Or, if your jasmine is already in a protected location, such as a covered porch or patio, just wrap the container in a thick blanket.