Look through garden design magazines and books to get some ideas about what you'd like to do with your slope. Take note of the options that are most attractive to you. Keep in mind that if your slope is steep, you may need to create some terraced flower beds and build some supporting walls with stone, brick, rocks or treated wood, according to the USDA Natural Resources Conservation Service (see reference 2). This will help rain to soak into the soil instead of eroding it.
If your slope is gentler, and you don't want to build steps or terraces, consider planting bulbs, ground covers, ornamental grasses, and flowers that will take hold on their own, creating a more wild, natural look.
Draw out a plan for your flower bed. Keep the drawing to scale and remember to plan according to the mature sizes of plants. You can determine the mature size of plants by looking at their tags at the nursery.
You may want to create a flower garden that is composed exclusively of perennial flowers, or one that incorporates ornamental grasses, ground covers, and trees and shrubs for contrast and seasonal variety. Spring blooming bulbs can be added for beauty and color when other plants are still dormant. Be sure to plan for color and interest in all seasons.
Remove existing sod and weeds from the area you'll be planting your sloped flower bed on.
Reduce the possibility of soil erosion by building a turf gutter at the top of the slope. According to the book Step-by-Step Landscaping, you need only to create a slight ditch with a lip on the downhill side all the way across the slope to direct water away from running down the slope, taking soil with it. Use soil and stones to build up the ditch, or strips of sod at the very top of the slope to disperse runoff (see reference 1).
Build and plant your hillside flower bed according to your plan, adding accents such as birdbaths and feeders, or garden statuary.