For a really good exposition on the matter, I would recommend Bl. John Henry Newman's, An Essay on the Development of Doctrine.
The Reader's Digest version is that Christ communicated all the essential truths needed for salvation to His apostles. Most of the essential components of that communication were contained in Holy Writ; however, as the Scriptures, themselves, testify (Jn 21:25), not all of Christ's words nor all of His actions were written therein. However, Christ promised His apostles (Jn 14:26) that the Father would send them the Holy Spirit to guide them.
As different situations came up over time, we can see that the Apostles applied their understanding of the teaching of Christ to that situation, even if they did not have His exact words dealing with that situation itself. At times, the apostles might not agree on these subjects and, on those occasions, they would call a council to deal with it. You can see an example of this in Acts 15:6-29 ("the Council of Jerusalem").
There have been many councils over the intervening 2,000 years. For example, the First Council of Nicea (in AD 325) dealt with the Arian heresy.
Over time, doctrine is developed and refined in this fashion. There may be a controversy and then something that was in Tradition is defined, which should, by rights, settle matters. Or there might be an issue that had never come up before and understanding HOW to interpret it is key: for example, the issue of embryonic stem cell research (there was no knowledge of cells, much less stem cells, 2,000 years ago). The point is that, as Cardinal Newman pointed out in the work cited above, you should see a logical progression of how the doctrine developed over time.
The big thing is that you don't just see doctrines pop out of nowhere. And you don't see them erupt on the scene just at random.
Hopefully that answers your question.
Also, I find it hard to believe that Christ's words or actions not recorded in Scripture can be adequately transmitted either by fallible men or their surrogates.
What I do believe is that the words and actions which the Holy Ghost has caused to be inscripturated are sufficient and completed for His use to guide (a/the) Spirit-filled human(s) throughout the interval until Christ Himself returns.
Perhaps reading the essay will illuminate an accepted view, as you indicate. I will do my best to scrutinize it.
Respectfully --