Hey there, Demian.
Firstly, the best way to proceed is to get in touch with a priest and get his guidance. While we can give you some general advice, we all need the guidance of someone who has been ordained, and thus has the special measure of grace, to guide us spiritually.
While there is value in things like facing an icon or facing east, the best prayer is the prayer that you do. No prayer requires any particular physical posture. What we need is a willing heart. "A heart that is broken and humbled God will not despise." I'm not saying not to face east or not to face an icon. What I'm saying is. To to ever let that stop you from praying.
The catechumen process is much like a wedding engagement. You've already met and gotten to know each other and have decided that marriage is the right thing, and now you're preparing for marriage. Similarly, we meet Christ and His church, we get to know Him, and we decide if being united to Christ through baptism is what we really want, and if we can bear the cost (not financial, but laying down our lives). Once we have gotten to the point where we can make that decision, we are then catechized and we begin preparations for baptism. As each person is unique, one person's catechumenate may be different from another's. But in general it involves one-on-one sessions with the priest, group instruction, and some reading. It also involves participation with the chirch's services as much as is possible.
As for myself, I was a Reformed Evangelical with a largely non-denominational influence in my earlier upbringing. I began studying Catholicism in my teens, which introduced me to the early church. For a long time I thought I would join the Catholic Church, but when I gave the Orthodox a chance to tell their side of the story, I started to find some holes in Catholicism, and I began to see that the Orthodox faith is that which has been handed down from the Apostles. I attended my first liturgy in March 2005, and I was hooked from the moment the choir first responded with "amen" at the start of the liturgy. Since then I have learned a lot of things, but what stands out is that the Liturgy can be as deep or shallow as I want to make it, and no matter how much times goes on, there is no exhausting its depth, and there is no exhausting the depths of her prayers and services. The more I prepare myself, the more depth I discover in her life that she offers.