In order for your jam to properly jell, or set up, you will need to include pectin when cooking it up. Otherwise you will cook up some fine-tasting thick blackberry syrup.
You can add commercially available pectin (follow the directions on the box), or take advantage of naturally occurring pectin - when you pick your blackberries, include some unripe berries, greenish-red and red rather than deep purple. The more sugar you add to your berries, the more pectin you'll need to cause it to set up.
If you prefer jelly to jam, as I do, crush and strain the cooked berry-sugar-pectin mixture while it is still hot. Line a sieve (one of those inverted cone-shaped ones that comes with its own wooden pestle is ideal) with cheesecloth and place it over a bowl. Pour in the mixture and crush away! Pour into jars. In my grandmother's day, jelly and jam jars were sealed with wax. This provided the young ones with a chewy little treat when the jam was unsealed later - a kind of homegrown chewing gum.
Here in the Pacific Northwest, we use Himalayan and Evergreen blackberries for making jelly and jam.