(From a letter to an inquirer)
Probably to begin with, I suggest that you get some icons (if you haven't already) and set up an icon corner or wall or space in your house where your family can say prayers together (and individually). Just one icon will do and it need not be an expensive hand-painted one. You can cut the icons out of the Orthodox Study Bible and put them on the wall. Icons are an important part of ancient Christian worship. Certainly we can pray without icons on the wall, but even words and (according to St. Gregory of Nyssa and others) concepts are icons. That is, words and even concepts are images that both point to the reality that they depict and participate in that reality. Icons are already a normal part of our lives. To take a simple example, you might have a picture of your wife that you keep in your wallet or that you keep on your desk at work or (if you wife is away on a trip) that you keep by your bedside. Although the picture of your wife is just paper and ink, it is more than paper and ink. Because it bears the image of your wife, that paper and ink participates in some way in the reality of your wife and points to the reality of your wife. When you honour the picture (by carrying it in your wallet or putting it in a prominent place) you are not honouring paper and ink, but what the image on the paper and ink represents as an icon.
Most Protestants and sects that came out of the Protestants are iconoclastic (icon destroyers). However, excavation has shown that the earliest Christian Churches and even Jewish Synagogues before the time of Christ had pictures on the walls. Even in the Pentateuch, God commands Moses to build images of angles and other living things for the Temple. This is in the very context of commanding Moses not to make images for worship as idols. I think one can safely say the second commandment, "you shall not make for yourself an image of anything in heaven or earth," does not refer to all image making. It refers to images made as idols. Otherwise, why would God command Moses to make images for the Temple?
A very important distinction for Orthodox Christians is the distinction between an idol and an icon. Many Fathers of the Church have written books on this distinction (I am thinking specifically of St. John of Damascus' Three Treaties on Divine Images [8th Century] and some of the writings of St. Gregory of Nyssa [4th century]). Briefly, an idol is anything but God Himself that one treats as an absolute. St. Paul says greed is idolatry because a greedy person "worships" whatever he or she peruses as an absolute, as something desirable in itself, as something for which he or she will sacrifice, or more often sacrifice others, to obtain. It is as if the desired thing (person, relationship, position, etc.) were god, an end in itself. An icon, on the other hand, always points beyond itself, and yet participates in some way with the reality to which it points.
St. John of Damascus introduces a distinction into the early Christian vocabulary. (Some background: in Greek, the word translated "to worship" just means to bow down to. This word is used in many different contexts. Sometimes (from the context) it is clear that this word should best be translated "to honour" in other contexts it is clear that it should be translated "to worship." This ambiguity was not a significant problem for Christians until their confrontation with Islam and the iconoclast controversy of the 8th century. End of background.) In the context of this spirit of iconoclasm that had come into the world, St. John makes a clear distinction between what we call veneration or honour and the worship that is due God alone. We venerate an image of Christ because the image participates in some way with the reality; however, the veneration "passes through" the image to the reality (the prototype) it depicts.
Furthermore, icons can be Spirit bearing. That is, the Church has taught from the beginning (and even in the Old Testament) that physical objects can be holy (sanctified) and carry Grace. So, for example, in the N.T. handkerchiefs from St. Paul were laid on the sick and they recovered. Or in the Old Testament, the bronze serpent made by Moses (at God's command) healed all who looked to it, and at the time of Solomon, the Glory of God fills the temple "so that the priests could not stand to minister." Similarly, icons (or any physical object for that matter) can carry divine Grace. This is an important concept not only because of icons (in fact, icons are a secondary consideration). It is important for Christology: understanding who Christ is.
If Christ is really, really both God and man (without change or alteration of either nature, human or divine) somehow the physical matter of his human body was able to bear (carry) the divine Person of the Logos. If we take this seriously, it has implications for all created reality. Thus we say in our daily prayer to the Holy Spirit, "Who is everywhere present and fills all things...." Now the depths of what this means and how we experience it is a mystery that we will spend eternity exploring. However, for the time being and considering our weakness, God has given us the Church and the Tradition handed down by wise and experienced Fathers (that is, experienced in their actual relationship with God). Icons, written prayers, feasts, fasts, liturgies, all of these exist to help us repent and come to know God better (by participation in Grace leading to sanctification). All that the Tradition has given us points beyond itself to the reality of God Himself; and by entering into the Tradition, we participate in that to which the Tradition points, and thus we are transformed.