Yes, eye contact is very very important. Notice for example that when you see a new girl and look into her eyes while she's looking at you, and you look away, she will immediately lose an interest. I noticed that many times.
* When you look away (to the sides) it simply says: I am not interested.
* When you look up it seems that you are dreaming; you might be quite confusing; you might be stuck in your head, simply not focused for the moment...
* When you look down you are signaling that you have low confidence, you are shy, your mood is down, you are submissive and so on...
So you want to ALWAYS give a deep look to a girl that you are interested in. You want to LOOK, not stare. You never look away, and never look down - not until she looks down (ideally) first.
The same thing with the girl:
* If she looks away, to the sides, she is not interested. At least not at this time. Think about it as she is "looking for someone or something else", especially if she doesn't look back at you
* If she looks up: she's probably dreaming, or you appear quite annoying to her, she is "looking over you"
* If she looks down she signals submission. It doesn't necessary means that she is interested, but there is only one way to find out - talk to her...
Sometimes she looks or stares "through you". It is just a trick, she is aware of the way you are looking at her and she tries not to move her eyes away or down. You can use the same trick if you are too anxious to keep looking in her eyes, but I wouldn't recommend it because if she finds out that you are looking "through her" she can easily put a label "weirdo" across your forehead...
But you shouldn't focus on looking into her eyes itself. The look is only superficial, it should only be result of your inner state.
Say a guy is very anxious and insecure but he keeps training himself in "looking" dominantly into girl's eyes. Ok, he might create dominant impression once he meets that girl - but what then? The first minute he starts interacting with her all this "dominant look" is gone, she will find out very fast that he is not confident at all. Now he keeps jumping with his eyes all over the place. His speech is nervous, he has his nervous movements of his hands, he laughs inappropriately, tone and pitch of his voice are fast and squeaky and so on...
There is also a chance that if he is too much focused on how he's looking into her eyes he will be staring, he will be forcing himself to keep his lids open while he is all anxious. You don't want to stare, you don't want to look like a hungry wolf. If you caught yourself staring at her, at least wipe your saliva from your chin, but chances are she will run away anyway because you just don't appear attractive at all...
So this sort of dominant look may actually work against him because she perceives him as a fake... It is actually much better not to pretend any 'dominant look', and just present the way you are... So this guy spends about 90% of his effort in giving dominant look, and his results are usually miserable...
On the other hand, you want to focus on your inner state first. You want to be relaxed, you want to feel confident and great. You want to feel sexy and ready for everything. You want to have great body language (erected yet relaxed), chest slightly out, arms freely next to your body (not covering any parts), both feet comfortably nailed to the ground. Your thighs are slightly outward. All your movements and thoughts are relaxed, your breathing is relaxed and slow, you breath all the way to your stomach. You are still, there are no nervous twitching in your body, and no nervous twitching in your mind. Like a fucking cowboy, just don't spit around.
How long does it take before you can say you are good at it? Practice every day, most of the day for the next three years. Then you know you are good. If guys notice that, you are doing too much, you are not relaxed enough, you appear as a threat and some will want to challenge you for no reason. You want to be invisible to most guys. But if only most girls notice that, if they give you exciting look and smile, that is when you are fucking good at it...
So this is the state you want to achieve first, then when you meet a girl you just look at her the way as described above. This time it is much different look because behind that look is all your inner state. It is real, not a fake. You look in her eyes gently and slightly smile. Your attitude should be "Hey, I really like you, I want to get to known you". Ideally she looks back at you and she should "melt" right in front of your eyes - because she mirrors your state right there. She should relax as well, she should smile and look down, and then she should get all excited because she met such a sexy guy... So this guys spends 90% of his effort in inner state, and only 10% on his look...