A few months ago I started attending the Orthodox Church in my community after being dissatisfied with my current church home and a few more that I had visited. I absolutely love it and I feel that this is the path that I need to continue on in my life.
Welcome to the Church and to the forum!
I have a few questions that I am uncomfortable asking church members. What is it that I suppose to be doing? How much do I need to participate?
I think the general rule is - attend as many Divine Liturgies as you can. Also, meet with the priest of your parish and talk to him, he will explain many things to you.
Do I need to venerate the cross? Do I need to kiss the icons? Do I need to do the sign of the cross?
I don't think anyone in the Church is "required" (forced) to do any of these things. One thing you might really want to do is watch the clergy (priest, deacon(s)) as they cense you or otherwise give you signs of blessing. It is a good etiquette to bow in this case, and also to cross yourself (although it's not a requirement, strictly speaking).
Do I need to cover my hair?
If you are a lady, watch how other ladies come to church in your parish. In some parishes, it is a custom to cover hair, so you wouldn't want to look like you disrespect this custom. In other parishes, women do not cover their hair, and then it's perfectly normal, I believe, for you to not cover it (unless, of course, you want to).
Do I need to set up an icon corner in my home or wait?
I would think you need it. The Seventh Ecumenical Council is very strong about praying in front of holy images. Your icon corner does not have to be very fancy though. It might be simply a small desk of lectern with one or two icons on it.
I have purchased some books to read about Orthodoxy but I am still unsure if I should be sitting and observing or participating on some level.
"Easy does it."