The first thing is to pick them carefully in the first place, discarding any stems and most bugs. The more exposed berries are easier to pick cleanly, as of course are the largest ones. Then with blackberries (for example) putting them in a large container of clean water can get rid of leaves and other bits of plant, which will float. I go for fairly high up berries in hedgerows along roads or even paths because they should be cleaner to start with and I don't want to strip the bush bare anyway.
Another method I use is freezing them (in a plastic box) until I'm going to use them. They're much more robust that way, and the bits tend to stay behind in the box, or you can shake the berries in a colander and rinse to defrost. Again make sure you don't put any stems in the box. This works in my case even for using a lot at a time (such as for jam or wine), because you don't have to gather them all at once.
But berries that have been frozen are less good for eating raw than freshly picked. So if you find ones that are small and tasty but not juicy, freeze them for cooking; big juicy ones: eat straight away. If you're camping or picnicking, you don't really even need to rinse them, just pick and eat, but look at what you're eating.