Mix one part peat moss to one part perlite and fill a flower pot with the mixture. When propagating the cuttings outside, combine the mixture with the soil in a bed instead of a pot. Work the soil well, so that it is thoroughly mixed.
Wear gloves to protect yourself from thorns. Snip a new-growth cutting from a healthy blackberry plant. Do this early in the year before the new growth becomes woody. Cut the cane 4 to 6 inches long, making sure there are leaves as well as buds on it.
Insert the cutting into the soil at least two inches. Position at least one bud under the soil and at least one leaf above it. Press the soil around the cane firmly and water moderately.
Cut the bottom from a plastic soda bottle and place it over the cutting. Leave the cap on the bottle. Press it into the soil so it forms a sturdy shelter for the cutting.
Place the pot in a warm location for five or six weeks. If you are propagating the plant outside, check that the plastic bottles are well seated, so they provide warmth for the canes and protect them from the wind and frost.
Check to see if there are new roots and new leaves on the cuttings in five or six weeks. If so, transplant them to the location you desire.