This is a very good question, and although I don’t have much experience (I struggle with relating to my villains too) I do have some theories based off of inspiring villains that I have read or watched.
I believe the main thing is to give them reasoning. Once a villain has a reason to do evil, you can then get the feel for how and why they do what they do. I got to see Ant-Man and the Wasp lately, and I liked what they did with the villain. Her name was Eva, and she had been hurt badly in the past by one of the main-characters. Her reasoning was revenge, and hopefully, to be healed from the wounds that were slowly killing her. I was able to sympathize with her, because underneath her “villain-ness,” she was just a girl who wanted a life like everyone else.
I think the second thing, like some others have mentioned, is to show your reader that your villain started, or is, like anyone else, they’ve just been corrupted. One of the most powerful examples of this is Gollum in Lord of the Rings. He was once a little creature like a hobbit, but not anymore. What happened to him would happen to Frodo, if the ring wasn’t destroyed. You can relate, and also add to stakes, by making the villain someone who is surprisingly similar to your Main Character, even with some of the same needs, wants, and interests.
I don’t know if that helps any, but those are some of my ideas.
Forgiven. Loved. Creative.