Suckering and tip layering are the easiest and most successful methods for the home gardener to propagate blackberries. Even beginners can successfully perform either, both of which have little if any effect on the parent plants.
Choose a healthy mature blackberry plant for propagation in early spring after all danger of frost has passed. New shoots, or suckers, will be growing from the base of the plant, and will have already developed their own root systems.
Sever the sucker from the parent plant with a clean, sharp gardening spade. Drive it deep enough into the soil to separate both root systems.
Plant the sucker in its new location immediately, and care for it exactly the same way as you tend your older blackberry plants.
Choose a large, perfect first-year stem of a healthy mature blackberry plant for propagation in mid-September. It should be thriving well and have no blemishes or damaged areas. The cane should have an approximate diameter of a pencil, and be long enough to easily bend over and touch the tip to the ground without damaging the stem.
Gently pull the tip of the cane downward and touch the tip to the soil. Make sure that the stem is flexible and that it doesn't show signs of cracking or bending sharply from the stress. Mark the spot in the soil where the tip touches, as this is where you'll layer it.
Dig a narrow hole 4-6 inches deep. Gently bend the selected stem over, insert the tip into the hole and firm it into place at soil level. If the stem looks like it may bounce upward and pull the tip from the ground, set a couple of rocks or bricks on the soil next to it. Remove them in a few weeks.
Keep the tip well watered so that the soil is evenly moist, but not soggy or waterlogged. In a couple of months, it will grow upward, develop roots underground, and emerge from the soil. Continue to care for the tip just as you do its parent plant.
Cut the parent's stem about 10-12 inches from the new blackberry plant in the spring. Dig it up and plant it in its new location. Take care not to disturb the roots any more than absolutely necessary.