Plant the jasmine in spring in a sunny, quick-draining site 4 to 6 inches from the base of the wall. The jasmine won't thrive in shady or muddy areas, or without good air circulation.
Amend the soil in your chosen planting site. Dig into the top 12 inches of a 2-foot-square site and turn 6 inches of organic compost or leaf mold into the natural soil. This addition gives the plant good nutrition, space and drainage for growing. Plant the jasmine in a hole just wide and deep enough for its roots, and pack amended soil around the base of the plant to secure it.
Put a wood or plastic trellis against the brick structure for growing support. Jasmine vines require this support, and can't "grab" the brick on their own. Use trellis netting for a less obtrusive alternative. Use a hammer and nails to secure a net trellis to the wall.
Tie the jasmine vines to the trellis in an upward and outward formation for best coverage, and let them fill in. Use soft cord ties on main stems, but don't tie leaves or flowers to the trellis; these break and damage the plant. Tie the main stems as they grow for continued training.
Water the jasmine with 2 to 3 inches of water a week during the summer; reduce watering to 1 inch of water every week in winter. Fertilize the jasmine with 10-10-10 granular fertilizer in spring for growth and flowering.