Blend the Vinegar, Honey, and Berries in your blender or food processor.
Slowly drizzle in oil while blending. If you have a blender that doesn't allow for adding while blending, simply add oil in small additions, a couple tablespoons or so at a time in between blending till homogenous,
You can strain this dressing through a sieve if you want a super smooth final product and don't want rogue chunks of blueberry skins throughout your dressing (though I find this an unnecessary hassle).