First, villains are people. Do not have a flat villain. Flat villains make flat films. They are only acceptable when used for ironic effect. They need motives, a background, and a system of self-imposed laws. Certain people don't do certain things. Only totally evil characters can avoid these, and those types of villains only work in horror and violent drama stories.
One of the best things you can do is make the villain relatable. Not like 'Okay, I'm would do that' kind of relatable. They are the villain. No. You want the audience, the ones who read into the story, to find the reason and the factors for the villains actions, and put themselves into the villain's place. You want the audience to look at them and say, "That's me." One of the reasons I like characters like Loki (MCU) is that the audience can understand his hatred for being the unloved, second-born, second-favorite child. They understand the bitterness behind him. That is one of the best ways to run a villain. Then the audience gets attached, and you can bend them by bending the villain. Look to Tumblr, and the fandom section's devotion to villains. We will find everything good about them. Do the fans of your story a favor and leave them some easter eggs. Leave tidbits of information that would come up with any character. Little mannerisms are the cutest things. Make the villain your masterpiece, the epitome of your writing skill.
As for introducing your villain to the story, it's good to tie them into the environment before we see them take center screen. Some authors can pull off a prologue being about the villain, showing their personality and/or power. This is harder in books than it is in films, as it's hard to pull off the 'Gas Explosion in London Apartment' in the background television thing that fans will go back and look at/for.
But villains should always have a good entrance. As good, if not better, than the protagonist's.