In no particular order of importance because they're all important:
1) Study of the history, reading the Apostolic Fathers, reading book 4? of Irenaeus' Against Heresies.
2) Being convinced over time that various claims of Orthodoxy have merit. The first one that got me was that the rest of Christianity is far too divided, too many denominations, too much confusion. You don't know where to go anymore to find the Church. The next was that the splits were caused in the first place because events such as the Schism and the Reformation made people think it was okay to leave/divide the established Church. After that, it's just one split after another, very unstable, with even the denominations splitting. Orthodoxy is a tree; Protestantism is a bunch of splinters.
3) Wanting a place where my wounded, sinful soul could finally be healed. I began to crave confession, where once I had thought it was a Catholic heresy. I began to crave fasting, prayer, and ancient worship. I began wondering how much of my life would have been different if only I'd had a priest to confess to and ask advice of. How many mistakes would I have avoided?
4) Prayer. I kept asking God to show me the way to go.
5) I wanted a place where I could be sure the Holy Spirit was speaking. I was sick and tired of hearing every doctrine, theory or desire defended as "the Holy Spirit led me to this." How can the Holy Spirit lead one person to say that homosexuality is wrong, and another person to believe God smiles on his relationship with his gay life partner? How can the Holy Spirit lead those who put the canon together, but lead another person to believe that the Bible only consists of certain books--and the books of Paul can be deleted? Etc. etc. Even before I considered Orthodoxy, I was sitting in a class on Issues in my PCUSA church, listening to various points of view about homosexuality in the church. During a question-and-answer session afterwards, somebody asked, "If everybody says the Holy Spirit told them different things, how do we know who the Holy Spirit really spoke to?" I had the exact same thought. And the preacher had no answer.