This will vary greatly from one society to another. In the U.S. direct eye contact is valued. A person who does not maintain direct eye contact, even on first meeting, is considered (rightly or wrongly) to be hiding something. "Look me in the eye and say that!" means that if the person is telling the truth, they will maintain eye contact. In other societies, especially those in which social class is important, direct eye contact might be considered an affront. A student that looks a teacher in the eyes would be considered rude. The only place this standard holds in the U.S. is in the military. A soldier is not supposed to look his superior officer in the eyes. In this instance, it is considered too personal and inappropriate.

Do you mean: "What do you look for?" I look for whether someone is actually paying attention to the situation and what others say, or are they lost in their head? Some people can't go for more than a few seconds before they are not paying attention, and thinking about their own ideas. As Gurdjieff said, most people are asleep. I look for whether the person is awake, or trying to be.

Most of the time, I look into their eyes. But sometimes, there will be other things that will draw our attention. Sometimes, it is the cloth they wear. Sometimes, it is the way they behave or talk. Interesting to observe others. Even people chatting online have their own manner or way to express themselves.

I look at their eyes