Usually people reproduce blackberries by cuttings, or my favorite lazy method, bend the end of a branch or cane down to the ground, and bury the tip of the plant. You can also use the suckers that spring up around the base off the plant as starts. If you cut the ends of the canes or suckers to use as starts, dip the cut end in root tone or a similar mixture before planting them in soil. As long as you keep them from drying out, cuttings should work well for you.
There are other ways of propagating blackberries, but these are the ones I've actually tried in the past.
