Is your character a sociopath, a psychopath, a person who snapped and became psychotic, or just someone who is plain evil? To know exactly how they would be diagnosed will help you to understand their pathology. Literally do the medical research on the person. People can have flaws they’ve acquired, or the defects can be ingrained in their nature. Know the case study that applies to them and how they are wired.
Let yourself realize how angry they are, so you don’t just play the generic rage of that character and stay on one note. And then find the layers of that rage. When does it come out in the story? Justify what makes them angry and how much power they crave, and how far they are willing to go to act on it. The amount of power they have after can be closely tied to their anger.
Think of all the choices you can make about how they hide their true feelings. Once you show the full dimension of a character’s fury, you have nowhere to go from there. The script will tell you when that explosion will fully erupt and that will usually happen at a climactic point for the character. All the other scenes are spent defending that. That is why you need to find creative ways to not show their wrath.
When you find the perfect attire, it makes for a colorful character. Villains are usually narcissistic and love hearing the sound of their own voice. A schizophrenic villain can have both a voice that is lighthearted, and another filled with vitriol. Costumes and voices are places where you can be highly creative.
Great actors don’t care if they are unattractive; they care that they are truthful to the character. Don’t let fear hold you back from finding and showing the monster within.
Everyone has a heart, so find your character’s soft spot. Be clear about a specific time in their life where they got their heart broken. That is what makes a character believable. The reality is that psychopaths cry and can feel (mostly for themselves, but it’s still feeling). Someone can commit a heinous crime and still be capable of a certain humanity. It is possible that those two extremes exist in one person. You can give yourself carte blanche looking for how they see the world. Humor is essential, and that can even contribute to making a villain likable—especially in a comedy.
Some have become archetypes. Watch some of your favorite characters and try to enact them. This would be a great way to study. When you find a multidimensional character to play, audiences will relish watching them and they will stay memorable.