The plants chosen for a new bed depend on sun and shade exposure, as well as how moist or dry the climate is.
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Choose a primary color scheme, consisting of two or three colors that look good together. Yellow and blue are complementary colors, so yellow cosmos looks really pretty with blue salvia. Purple and orange also work together nicely. Purple pansies complement orange miniature roses. You could also create a rainbow-confetti look with many different colors but you really need to know what you're doing or it could look like chaos. You're much safer picking plants with compatible colors that offer different textures and shapes.
Mimic the surrounding landscape, using different types of plants to add dimension. Brightly colored annuals and bulbs work well for these beds, providing color and seasonal interest. Add some contrast with ornamental grasses and plants with interesting foliage like dusty miller and various variegated perennials and shrubs. Evergreen shrubs, like Pittosporum 'Wheeler's Dwarf', provide a nice backdrop for the colorful flowers too.
Arrange plants by height. Put the lowest plants in front and the tallest plants in back. You'll get a better view of each plant and it will have a three-dimensional look instead of looking flat. Planting them in groups instead of rows will look more natural too. Space your plants close together so their "shoulders" will touch when they grow in. This way your bed won't look bare in spots. If you're planting bulbs or annuals that will need to be replaced season to season, place them in the front so they're easier to get to.
For the final touch, add mulch around the plants. This will give it a clean, tidy look and complete the new bed.