The doctrine of the priesthood of all believers does not mean only that we can pray directly to God, though it does mean that. And it does not mean only that we can read the Bible for ourselves, it does mean that. But it means primarily that we have a holy, happy duty to worship the living Triune God and to do it as priests.
Our worship is intercessory. Priests represent God before the world and they represent the world before God. Read more