There is, but it's been at least two years since I took any sunday school so I can't rightly remember the official answer.
To the best of my ability, I can say, looking around at my own icons, that most often a saint depicted alone in an icon will either be looking directly, as if to see you, or skyward, as if to God. If there are many depicted in one icon, most often the 'leader' so to speak will be looking at you, while the rest look to the leader, or also skyward to God. (This is how I see most Romanov icons, with Nicholas looking at you, sometimes also Alexei as Tsarevich, and the rest looking toward one of them. Occasionally though, everyone is looking directly.)
Icons were originally created for illiterate people, to share the word of God to those who couldn't read the Bible. So many icons tell stories. For instance, Andrei Rublev's "Trinity" icon depicts the three angels are looking at one another, in a balance. Every little detail in an icon means something, so it's hard to remember everything. For instance, again, in Rublev's "Trinity" the feet of the two foremost angels create a chalice shape, in obvious representation. The colours everyone wears each have meanings too. You can see how I could go on and on.
I hope I helped?
