Confronting the Shadow is an important part of every witch's journey. It is very difficult, but a necessary step in anyone's spiritual development.
Shadow work is the process of acknowledging, coming to terms with, and eventually integrating "dark" or repressed aspects of your personality. Usually, these aspects are repressed because you feel ashamed of them for whatever reason, to the point where you try to disassociate them from your conscious identity. When you encounter them, in yourself or other people, your knee-jerk reaction is, That's not me, that can't be me. But it is you. Ignoring your Shadow and disassociating it will not make it go away, which is why it must be addressed and reintegrated into your conscious personality. It's not easy to do that, for a lot of reasons.
First of all, it's really difficult to realize what these repressed aspects are in the first place because... well... they're subconscious. In Jungian psychology, the recommended method of doing so was paying attention to projections — if you irrationally hate someone, it may be because they are exhibiting behavior or personality traits that you possess but refuse to acknowledge. If you get defensive when confronted with this person, or when someone suggests you might be like this person, or when you consider if you have similar traits, that tends to be a dead giveaway. Anything you get defensive about likely is rooted in something Shadow-related.
A phrase I've been using lately is "We are all our own inverses." I don't think it's accurate to say that your Shadow is your opposite. It's not your opposite, because it's definitely still you. It's you, but... backwards. It's still too much like you to be the polar opposite of you, but it reverses your values, which makes it much more disturbing. For example, I value free will and equality, so my Shadow is a tyrant who elevates and glorifies himself. Your Shadow self is like a dark reflection of your conscious self. It is simultaneously everything you're not and everything you wish you could be. Because the Shadow conflicts with your perception of yourself on such a personal level, accepting that it is you is absolutely brutal. I say that "if you're not screaming in anguish, you're not doing it properly," and although I say that partially in jest, Shadow work usually does cause an earth-shattering existential crisis the first time.
To illustrate what I mean by that, here is a chilling animatic that I found on YouTube. It is based on the musical adaptation of The Strange Case of Dr. Jekyll and Mr. Hyde. I was speechless the first time I watched this. I think that this video perfectly demonstrates what Shadow work can feel like at its most difficult:
It's important to keep in mind that the situation being presented here is a very dramatic and drastic one. At this point in the story, Hyde has murdered people, and Jekyll is understandably horrified. But Jekyll also fails to take responsibility for his own actions as Hyde, which further distances Hyde from himself and makes him more dangerous. In true Shadow fashion, Hyde taunts Jekyll to make Jekyll accept that they are the same person. "Don't you see? YOU ARE ME!" When Jekyll refuses, Hyde takes over by force. So, this video is also an example of what not to do. You have to be able to take the high road and admit that your Shadow is you. Embrace it and love it instead of shunning it, and that will give you control over it. Your experience with your Shadow probably will not be this traumatic, but it will likely feel this traumatic, so I still think it's a good example.
Exactly how you do this depends on whatever works best for you. You could use meditation and trance, therapy sessions, some form of divination like automatic writing, masturbation (a lot of Shadow baggage pops up during masturbation if you really let your mind wander, since it is a means of achieving trance and sexuality is often repressed), etc. Just do whatever works for you.
My own method of dealing with my Shadow was to personify him into a character, whom I am writing in my novel, Shadowbook. Actually, I didn't create him deliberately... he just surfaced. He told me his name. The name Astor just floated up out of my subconscious and asserted itself. I didn't decide much about Astor's appearance, either. I gave him violet cat eyes, but otherwise I made very few conscious decisions about his appearance. (His first iteration had short hair. Oh, the horror! Now he has long, flowing hair and that's not about to change anytime soon.) Astor is a prince. I did officially decide to make him a prince in my novel, but in hindsight, I realize he was always a prince. What better explains his arrogance, his hedonism and appetite for luxury, his desire to be worshipped, his domineering presence, his desire to subjugate others?
And yet, despite all of the ways that Astor and I are opposites, Astor is still me! He has the same aesthetic and appreciation of beauty, the same violent mood swings, the same love of dance and literature (and cats), same passion, same authenticity, same good performance skills but poor social skills, etc. (In the novel, I've also given him my sense of empathy, so that he has some redeeming qualities.) He's my self-insert. I'm still working through some stuff with him (for example, the way he treats women still really disturbs me), but in general, I have become familiar and comfortable with my Shadow. Through writing him, I can engage with my Shadow in a way that's safe and healthy. In a spiritual sense, Astor has become one of my most valuable assets. Astor is an entity, a twin spirit to mine. He is my constant companion, my familiar, my lover. I interact with Astor on a regular basis and I love him very much. He provides me with information, advice, and emotional support. I have him invoked often, and I usually assume his identity when I astral-travel. I literally would be incomplete without him.
You don't have to personify your Shadow to such a degree if you don't want to, but once you have your Shadow figured out, it's still a good idea to find some sort of safe outlet for it. This could be writing or creating some other kind of art, playing video games, acting, role play, sex or BDSM, exercise, living out in the wilderness for a few days, etc. Once you get to know your Shadow and accept it as part of yourself, you will be able to control it, and you won't be afraid of it if you encounter it in other people or entities.
The reason why this is important as a spiritual process is because any significant spiritual work requires this intense level of self-awareness. You can't reach enlightenment if you're projecting your own demons left and right. You can't transmute yourself into a higher form if you haven't addressed the personal baggage you're dragging around. You can't do any productive work with darker entities who might drag up, embody, or try to take advantage of your repressed Shadow if you haven't dealt with it. A dark god will likely slap you in the face with your Shadow to get you to confront it, which is painful (see above), while a demon might manipulate you by playing off of your projections and insecurities. If you've done Shadow work, you can move past that.
When the villain proclaims, "We're not so different, you and I," he expects the hero to be thrown off-guard and have a big existential crisis or mental breakdown. If the hero has done Shadow work, though, his/her response will simply be "Yeah, I know. Are you done?" When confronting the many trials of the spiritual world, you want to be that person.