By and large, it is the whole church guided by a representative assembly of some sort, drawing from the learning of Bible experts, theologians and other scholars. In other words, not a lot different from how your church arrived at its conclusions.
Of course, there are freebooters or lone wolves who insist that they don't need a church...and they are always classified as Protestants, but it is grossly wrong IMO to characterize what such people do as the way Protestants proceed. There are Orthodox Christians, too, who have some unorthodox beliefs that their churches never taught them, either.
I hope that my answer above covered that. Protestant churches are not institutions where anyone of any belief just shows up, believing whatever seems okay to him. Unfortunately, people think Protestant, for being such a broad generalization, means 'anything goes,' whereas the same problem for a Catholic or Orthodox Christian is brushed aside by saying "Oh, they are heretics. They don't count."
Fair enough.
At times I think perhaps the label "Protestant" is not particularly useful. For the way we function when we discuss such things, those lone wolf types ARE Protestant, yet as you say, not all of Protestantism can be understood that way.
I think we come round in circles. Yes, some do agree with the teachings of their denomination, established confessions, and so forth and in that respect they function as the Orthodox do, just substituting something more recent, or perhaps supplementing, the early Church teaching. So they have quasi-councils or quasi-popes, just different ones. But then how is their Sola Scriptura different from Orthodoxy, say, except in the seat of authority?
And there is a very broad segment that fall under the label of "non-denominational" or are otherwise independent, whose doctrine as a community is usually decided by one man.
Maybe all of this just clouds the issue. I don't know of anyone, Orthodox or Protestant, and as far as I know, Catholic either, who denies the authority of Scripture. (Well, I take that back, I do know of a few scattered individuals but they don't represent anything we need to consider here.)
But when it comes down to whether those Scriptures speak of Christ ACTUALLY PRESENT in the bread and wine, or mere symbolism. Of salvation that requires perseverance, or whether it is impossible NOT to persevere. Whether baptism is a means of grace, or just a public statement. The role of women in the Church. And a thousand other questions - there is disagreement. And ALL will point to the same Scriptures (seen through their particular lens or that of their denomination) to justify their dissenting answers to those and many other questions.
It never was really about the authority of Scripture. It really boils down to whose interpretation of Scripture, in every case.