Blackberries don't grow as bushes: they are climbers/vines. That's why you need to train yours on a trellis.
There are several ways to train them (chiefly to make picking easier) but, generally speaking they are such vigorous plants they really need pruning.
Pruning serves two purposes on blackberries.
First is to keep their size in check: wild ones around here will easily grow over 15ft.
Second is to encourage blooming and hence fruiting: blackberries produce flowers on their new growth.
After you chose which shape to give to your blackberries, you can prune them heavily, no need to use the kiddy gloves. A 7ft plant can be easily cut down to 4-5ft. Any time is right, except when they are blooming: you can do it now or later in the Winter.
Three pieces of advice now.
First, generally blackberries are not fertilized, both to avoid them growing to monstrous proportions and because they seem to do better in slightly poor soils. If you want to increase yield you may w-a-n-t to use a nitrogen-free (PK) fertilizer, but it's not really needed.
Second, blackberries are very drought tolerant but more water will usually result in sweeter, juicier berries. Water them regularly if the Summer is dry, especially when the berries are starting to grow.
Third, blackberries are one of the most invasive plants I have the displeasure of dealing with. Birds will readily disperse the seeds and since the seedlings are extremely shade resistant and will readily regrow if cut to the ground they are difficult and time consuming to get rid of. Always harvest all you blackberries, don't leave any to the winged critters.
