My simple answer: the Holy Spirit promised to guide the Church into all truth. The Orthodox believe that He has fulfilled His promise. Now for my lengthier response:
There is somewhat of an implied dichotomy in Western thought that must be called out right off the bat: the distinction between Scripture and Tradition. In Eastern thought, there is no distinction, as the Church and its apostolic tradition existed before the New Testament was written. Scripture is part of tradition, indeed it plays the preeminent role in Tradition. Tradition is not opposed to Scripture nor does it contradict it any point, rather it explains Scripture. But I do not have time to address this fully, nor is it exactly the question at hand. Suffice it to say that in Eastern thought (and increasingly also in modern scholastic Western thought), sola scriptura is a myth-a logical fallacy. Everyone appeals to tradition when interpreting scripture - we just don't agree on which tradition, and many deny that they have any such tradition (and this ignorance is even more dangerous). Hence the 23,000+ denominations in Western Christianity.
In John 16:12-13, Jesus said, "I have many more things to say to you, but you cannot bear them now. But when he, the Spirit of truth, comes, he will guide you into all truth." It should be noted that in both instances, the word "you" is plural. This promise was not made to individuals, but to the disciples, they that would become the Church and form the apostolic tradition that was to be guarded and passed on (cf. 2 Thessalonians 2:15; 3:6). Keep in mind that many churches were planted before the New Testament was written.
When early heresies threatened to corrupt the gospel, early Christians turned to the apostolic tradition to defend the faith (such as when Christians appealed to apostolic succession to refute the Gnostics' claim that Jesus had secret teachings and that there were alternate gospels. Note that no official canon of scripture was adopted until the 16th century in the West, and no official canon has ever been declared in the East). When heresies threatened to divide the unity of the entire church, the church came together with bishops (episkopoi) representing the Church in various geographic regions, including both East and West for the first seven "ecumenical" (church-wide) councils.
When considering this question which was directed to the East, a broader one comes to mind: how can anyone in Christianity-whether Eastern or Western-be sure that the Church's decisions are correct and not erroneous? For instance, the Church preserved certain texts which were eventually accepted as the canon which we today call the bible, and they chose to repudiate other texts. Even still, not everyone was unanimous on the 66 books included in the modern Protestant bible (cf. antilegomena), not to mention the deuterocanonical books found in Roman Catholic and Eastern Orthodox bibles. The reality is that everything we have in the Christian faith, including our bible, comes from tradition. Studying history helps make sense of it (I highly recommend Jaroslav's five-volume set on The Christian Tradition: A History of the Development of Doctrine, and his concise book Vindication of Tradition. Pelikan is a renowned ecclesiastical historian).
The East has critically evaluated the Church's many theologians, such as the Cappadocian fathers repudiating how Origen and Irenaeus integrated Platonic and Neo-Platonic thought into their theology. Also note that with the exception of Martin Luther and some recent scholars, most Western Christians have never considered how Aristotelian thought and scholasticism has impacted Protestant theology. Western Christianity's ignorance of history prior to the 16th century has lead them to unquestionably adopt many heretical and worldly philosophical viewpoints, and this can be seen clearly in the rampant division and individualistic soteriology that has marked Western Christianity.
A close examination of history shows a remarkable unity in the history of the Church for over 1000 years before the bishop of Rome excommunicated the patriarch of Constantinople in 1054. Prior to that event the Church had always decided issues via ecumenical councils, but the bishop of Rome wished to have sole authority over the entire Church, which was an innovation and was not the apostolic tradition (contrary to Roman Catholic teaching that Peter was the head over all the apostles-we can see already in the New Testament that Paul corrected Peter and that James appears to preside in some way as a leader over the Jerusalem council in Acts 15). Suffice it to say that while there are anomalous events such as the council of Hiera, history shows that these decisions were local and thus not widely accepted and passed on in the Church. Despite many challenges to the faith and Church unity, She maintained remarkable unity throughout history, especially in the East.
In summary, the East trusts that the Holy Spirit has continued to guide the Church into all truth. Eastern theologians are generally very knowledgeable about Church history and they "give their ancestors a vote" when interpreting scripture. Most Protestants do also, they simply aren't honest about it in most cases and don't look much further in the past than the 16th century for theological guidance, except to occasionally use the content of early conciliar creeds.
I do not have time to write a history lesson about the many interconnected issues that are requisite knowledge for a more in depth discussion of the trustworthiness and value of tradition, I have merely hinted at some of the notable data. I hope that I have given a basic response and good resource recommendations to learn more. I hope that this response has not come off as demeaning. I frequently hear Western Christians critiquing Eastern Christians for being uncritical towards Christian history, when the exact opposite is generally the case.