The importance of the eyes is highlighted especially in close-ups. Michael Caine created a very specific eye technique. Michael Caine never blinks (unless specifically required by the character). Blinking makes your character weaker, takes you off the pedestal and people won't listen to you. This is not, of course, a universal rule (no rules are universal); Hugh Grant made of blinking his trademark. You will never see Hugh Grant in a shot where he doesn't blink to exaggeration. Smart move for a number of reasons: he was the first to do it and, as such, everybody noticed it (and I believe that the only way to "make it" is to find an original way to be noticed); secondly, he is able to convey contradictions and idiosyncrasies by means of his blinking. Michael Caine warns actors never to shift eye focus from one eye to the other when shooting a close up. When looking at something, one eye always leads. Change leading eye and the camera will notice it. Another trick he discovered to make close-ups more effective: in close-ups, he will focus on the eye of the off-camera actor that's closer to the camera, using as his own leading eye the one that's furthest from the camera. This little gimmick enables the actor to have as much of his full face as possible in the shot.
Henry Fonda was well known for involving his characters' personas in a melancholic aura. It all starts from his eyes, which in close-ups always reflect a dim, sad gleam obtained with what he used to call "inky-dink", a tiny light the lighting guy was instructed to always keep up before his eyes in close-ups.
One crucial exercise for aspiring actors is to observe the way other actors use their eyes. It is all about acquiring awareness over this powerful tool and learn to use it in the proper way. But most important, observe people in real life situations. Observe them on the subway; observe the way a man's eyes shift from the newspaper to a beautiful woman sitting or standing right beside him. Observe the stealthy way he tries to look at her trying not to be noticed. Observe how, after a quick glance, probably at her attributes, he subtly looks around himself to see if someone noticed him looking at her, before he goes back to his newspaper. Look at how people look at themselves as they talk to each other at a restaurant. Look at how people stare in the void on the bus and how they get up ready to get off still staring in the void, until they are really forced to focus on the direction they are headed to.
As an aspiring actor myself, this is all I can do. Observe, remember, try it myself at home, and bring it to application when I'm shooting.
If actors use their eyes in the proper way, they don't need to pull faces. Pulling faces is a cheap way to let someone else know that we are feeling something. Pulling faces lacks spontaneity and it amounts to wasted energy, when everything can be obtained with simple and proper eye work. But like I said, no rule is universal: Jim Carrey is the king of pulling faces. He made it into a technique, a trademark of his own acting system, of his own persona, his brand. And, honestly, is Jim Carrey's pulling faces out of place in his movies? Arguably enough, not at all!!