Raspberrys and Blackberrys grow on 2, 3 and possibly 4 yr canes. Removing 1/3 of your oldest growing canes every year should give you plenty of berries. I fertilize after harvest for the next years push.
Generally speaking for fruit trees (actually any tree), clear out any branch that grows inward towards the center or upwards. Also remove the weakest of two crossing branches.
On other branches look for the fruit buds and prune off one segment out, leaving the newest growth at the end of the main branch alone. Keep an eye out for too many fruit buds on one branch. They could be thinned out.