Fall-bearing raspberries can be managed for two harvests, a small summer one and a small fall one, but are more easily managed to have just the one starting in late summer and running until frost. If you want to double crop them, you prune the fruiting canes halfway after the first crop and to then prune those canes to the ground in November. This will require trellising the crop. For the larger fall crop only, cut all the canes to the ground each November. This also minimizes disease and trellising.
Black raspberries are in a class of their own.
Much of the culture is the same, but the productive period is 2-8 years. They have a sweeping growth habit and tip root readily. New canes are usually tipped at 3'. All canes which bore are cut to the ground. They are best cooked, being used for jams, jellies, wine, pies and dyes.