Clear the slope of weeds and grass with a shovel as you would any garden area. Amend the soil with generous amounts of compost. Add peat moss to improve soil retention of moisture and nutrients. Turn amendments into the soil with a spade.
Water the area with a hose and watch where the excess water flows and divert it, if necessary. On very steep slopes, build terraces or steps to divert or redirect excess water, or prevent erosion by installing pathways into the slope in strategic places, which also serve to channel runoff water.
Dig a hole for each plant an inch or two wider than the width of the root ball, so the roots can be spread out, and deep enough for plants to sit at about the same height as they were in their nursery containers.
Remove plants from their containers and place them in the holes.
Cut the bottoms out of the containers with a utility knife and cut them down the sides into two pieces. Place container pieces around the outer edges of the holes, to form a collar that will help to retain moisture at the base of the plant and deflect excess moisture coming down from the hill above. Fill in the hole, leaving the collars above ground. Use paper cups for collars when planting small plants or seedlings. Collars may be removed once plants have established strong root systems.