Before you put a spade in the soil, make a plan. Decide whether your triangular bed will be formal or informal, flowery or mostly green. Prepare the site. If it already has plants, weeds or grass, remove any plants that you want to save, cut off all the rest flush with the ground and smother with a layer of landscape fabric topped with several inches of mulch. This can remain in place until you are ready to plant.
If the triangle's sides are equal, anchor the bed with a central focal point. This can be an evergreen, a bird bath or a sculpture. Choose the anchor first and plan the other plantings around it. For example, use a dwarf Hinoki cypress (Chamaecyparis obtusa "Nana Gracilis"), which grows in U.S. Department of Agriculture plant hardiness zones 4 through 8, as an evergreen focal point in a bed that is 18 feet per side. Edge the triangle with low-growing Korean box (Buxus sinica var. insularis "Wintergreen"), which grows in USDA zones 4 through 9, for a formal effect.
If the sides are unequal, or the orientation of the triangle is significant because one of the angles is at the front of the bed or points at another important landscape feature, position the focal point there. This can be a tall feature like a climbing rose such as "Zephirine Drouhin" (Rosa "Zephirine Drouhin"), which grows in USDA zones 5 through 9, trained on a pillar and surrounded by shorter species. Always make sure a tall anchor feature or plant does not interfere with important sight lines, as in the case of triangular island beds at traffic intersections.
Before choosing plants, know the sun or shade exposure of the site. If you are inexperienced about soil types, buy a soil test kit from a garden center. Knowing the soil type will help avoid costly plant selection mistakes. The size of the triangular bed will also determine access issues. A large bed may require a path or at least a network of stepping stones or pavers so plantings can be easily maintained and visitors do not walk on the plants.