Berry plants tend to be fairly low maintenance plants, put them in the right place, keep them watered and they will grow stronger, bigger and more productive every year (until they threaten to fill your whole garden and you have to start restricting them). Even so, there are a couple of things you can do to help your plants and increase the harvest for years to come.
In most places the most important thing you need to do for your berry plants is protect them from birds. Birds love berries just as much as you do (after all, berries were created to be eaten by birds as a way of transporting the seed). If given the opportunity they will strip the bushes of every edible fruit. You could try various ways to scare them away — shiny tape, inflatable predators, scarecrows — but birds will soon figure out that these aren’t a problem, so they don’t usually work for long. The only foolproof way to foil the birds is by carefully covering the plants with netting (this has to be done thoroughly because they will look for any openings). Applying and removing netting is a real pain because it snags on everything it touches (be careful it doesn’t tear) and is one of the few garden jobs I really dislike. If you have to do this every year, you might think about putting your berries inside a permanent fruit cage (the simplest of these is made from PVC pipe).
The other important maintenance activity is removing old stems to encourage vigorous new fruiting growth. Blackberry and raspberry canes usually die after their second year and can create a dense thicket if not removed (these can be removed after they have finished fruiting). Blueberries and currants fruit more vigorously on younger wood, so every year some older ones are removed to encourage new growth.
To keep the plants growing as vigorously as possible, you also need to keep them well watered. Keep the soil moist, but not wet. If the plants are bearing heavily then some fertilization may also be needed to keep them producing well. The best way to do this is to apply some mulch, which will also keep down weeds and conserve moisture. Just be sure to use an acidic mulch such as pine needles for blueberries, since they need a bit more acid.