In some ways, the antagonist may even be more important. Your main character cannot become sympathetic without an opposing force. The antagonist is more than just a bad guy who tries to stop the good guy. A good antagonist actually pushes the protagonist to action. The bad guys gives the good guy a reason to behave like a good guy.
Because he is so important, your antagonist has to be every bit as real, every bit as well-rounded, as the protagonist. So how do you do this?
No. The good antagonist is not evil. OK, he could be, but not for the mere sake of being evil. The antagonist truly believes he is the good guy. Everything he does has a reason, and to him, those reasons are Right. They are Correct. They are Good.
Few characters are as flat and dull as the arch-villain who is evil just because being evil is evil. People aren't like that. Even people with a warped sense of reality (and here's a little secret: we all have a warped sense of reality, shaped by our own histories and imperfect perceptions), do things for a reason.
There are truly evil actions, and your bad guy might do some of them. But we humans have an almost unending supply of rationalizations for our actions. If we're honest, we recognize that sometimes the way we rationalize our actions is often, at best, flawed, and at worst, just plain delusional.
Just like you want your good guy to have flaws, you need your antagonist to have positive characteristics. In some stories, the reader might even start to wonder just which character is the good guy and which is the bad guy. The line doesn't have to be a thick one.
A Rebel With a Cause
Your good guy is on a mission, a quest to accomplish something. The same is true of your bad guy. Your antagonist has his own character arc. Character development is as important to your antagonist as to your protagonist.
So give your antagonist a cause. She wants to accomplish something, wants that more than anything else. And, like your protagonist, she is prepared to do what she has to do to achieve it, because that's what people do when something is of ultimate importance.
Even a bad guy who wants to do something truly awful, like, say, blow up a stadium full of innocent people, does it because he believes it has to be done to achieve the goal. He probably doesn't enjoy doing it, but feels it is necessary and does what has to be done to achieve the end result, which he believes to be for the ultimate good.
Most antagonists act in smaller ways. It's easier to justify the actions of somebody who is competing with your protagonist for the position of Head Cheerleader or who wants the powerful amulet for himself.
A Hero in His Own Mind
Because the antagonist believes what he is doing is the right course, he believes he is the hero. Or, at least, he is trying to become the hero. Your protagonist, who stands in his way, is the villain. My favorite example of this principle comes from politics. No matter what your political position is, you view the other side as wrong. Maybe even evil. The thing we don't always accept is that the other side looks at you the same why. Why? Because each side believes it is right. Each side believes it is the hero, and if they were only allowed to have their way, the world would be a spectacularly better place.
The other side is only "wrong" because you happen to believe in your own candidate. Chances are, you don't admit your own candidate's flaws, or at least not the big ones that the other side tries to highlight. Whether you want to admit it or not, the other side probably has a point, and the criticisms may well be justified. But you're committed to your side, so whatever faults your guy has, the other side is exponentially worse.
It's the same with your hero and villain. Switch to your villain's point of view and he is clearly, obviously, without a shadow of a doubt, the hero. Let your reader see that.
Let your reader sympathize with the antagonist, and understand why he wants what he wants, and maybe even see his point. Maybe you don't want your readers to agree with the antagonist (or maybe you do), but if your reader can sympathize with both characters, the conflict becomes more real, the stakes are raised, and your reader is more engaged.