Running an evil campaign in an rpg.

Goals and Desires

As with any other campaign, defining character and player goals and desires is always a good start, but perhaps more so in an evil campaign. If one player wants to play a game of intrigue and subterfuge while another player wants to kill as many characters as possible before being taken down in a blaze of glory, balancing the campaign will be difficult without this prior knowledge and some planning. By taking into account what both the players and their characters want, weaving them into a cohesive whole will be much easier and often provide a more satisfying game for the group as a whole. A game of subterfuge could lead to moments where all the NPCs needs to die to prevent witnesses, for example, so the murder hungry character will get to shine here.

The character's desires and goals are incredibly important for a balanced group. While in a regular group you can often have a character or two who don't quite fit in, but are willing to work with the group, in an evil campaign you can often encounter characters who plan on backstabbing the others, characters who only care for themselves and refuse to cooperate with others, and a whole range of others who make playing as a group difficult. To avoid this the players in your group simply need to create characters who are willing to work with or for others. This can be achieved in all sorts of ways. Payments, mutual beneficial goals, returning favors, potential for loot or riches, gaining social standing, blackmail, security through numbers, and so on.

Characters you'll want to avoid generally fall into the lone wolf category. It doesn't matter if this come in the form of a powerful noble who refuses to work with commoners, an edgy character who feels they're too good for others, a chaotic character who only seek to ruin everything they can, or something else. They're all disruptive and end up being more of a one player game within the group. This doesn't mean it can't work, it could if the entire group is willing to engage in more personal stories without the involvement of most of the other people.

An example of how this could work is through various crime syndicates ruling different parts of a city. The players will likely work with and against each other, each trying to gain control of the entire city while also each engaging with NPCs for various purposes. These same NPCs may back-stab the players' characters by working with those of other players or even selling them out to law enforcement should the deal be sweet enough.

Character Choices

It's easy to fall into the trap of making a character evil for the sake of being evil within these campaigns. While this can be fun for some, those who seek more role play depth may want to think more about other elements of their characters. You can be evil and care about people or things, you can be evil while still showing mercy or emotions, you can be evil and be reasonable. Take Thanos, for example, (spoiler alert for Avengers: Infinity Wars, skip to next paragraph to avoid it) he sought the power of the infinity gauntlet in order to wipe out 50% of all life in the universe so they wouldn't destroy themselves by using up all resources on their respective planets, which he saw happen on his own planet. He was definitely evil, but also a complex character who was capable of love and reasoning unlike some super villains.

Characters who are evil for the sake of evil are usually very predictable, even the ones who back-stab people generally are. Because of this they're often less fun for people to play with or as because it can take away the role play element to a large extent. Characters who are like this are also often aware they are evil and may even take pride in it, but the best villains are often those who see themselves as the hero in their own story. This isn't always true of course. The Joker is an evil character who knows he is evil, but is still a developed character enjoyed by many.

In the end it all comes down to what you or your players want. Some are happiest playing an evil caricature who seeks to cause as much chaos and destruction as possible, others prefer Game of Thrones levels of depth, mystery and betrayal. Simply make sure the entire group is aware of which way the game will likely go so everybody can make character choices accordingly.

Consequences

A big element of evil campaigns is how you as a game master (GM) deal with the consequences of the player characters' actions. Murder is unlikely to go unanswered in most campaign settings, but in an evil campaign you may need to skew the rules of your universe a little to favor the player characters depending on their goals and desires. At the same time, keeping the rules real can add a lot of tension and urgency to the game. It again depends on the group.

If your group wants to have more freedom to cause chaos without being chased by guards or the law at every step, you can accomplish this through world building that sets different rules in a realistic way. If you're playing a game in a medieval fantasy setting, for example, usually a king wouldn't let the brutal murder of a village go unanswered. But if the king is in the pocket of the group, there's not much he can do. Innocent people (or different criminals) may be used for public displays of justice while the true criminals continue their path of destruction.
There will likely come a time where the people have had enough of the violence in the kingdom and seek to overthrow the king, but this can lead to more ways to create chaos for the party as well as some political intrigue.

If your group prefers real consequences for their actions, the game works best when deception, stealth and similar themes are used. A Game of Thrones-esque setting could work well, for example, or the before mentioned criminal empires or dirty cops in a law enforcement agency. Any setting where characters have some form of established power they can use to get away with their crimes works. It doesn't matter if it's a royal power backed by an army, a clean public image with a lack of evidence of the committed crimes, a law enforcement agency that will simply destroy or fabricate evidence as they see fit, or something else entirely.

Quests and World Building

I've already delved into bits of world building so far through potential story focuses, but I'll go a little deeper by focusing on quests. Political intrigue is great and all, but not every GM is up for creating everything that comes with it or keeping track of all of it. So what alternatives are there when creating an evil campaign that isn't just a hack and slash until you perish type of game? The easiest way is to simply use regular quests as you would create in any regular campaign. Evil characters will find a way to steal the artifact they're meant to find instead of delivering it, or enslaving the monster they're supposed to save a village from, or selling out the person they were hired to protect, or simply moving on with the advance payment they were given.
Alternatively, reflavoring your quests for evil purposes works too. Protection quests turn into assassination quests, retrieval quests become theft or destruction quests, gathering quests become gathering quests of souls, blood, innocents or whichever unsavory goods the quest giver may need, and so on.

What about world building though? World building for an evil campaign isn't all that different from regular world building. The pieces you build may be different, but the methods are the same. The thing you will want to keep in mind is how evil the world you make is. The more evil it is, the less contrast between that world and the evil acts of the group. This matters when players aren't all that comfortable playing an evil character as it's a lot easier to do so in an evil world. Destroying and killing a village of innocents as a show of force is one thing, doing the same to a village of people who either willing participate in the selling of children as slave labor or who just let it happen is another.
Likewise, the consequences of killing a village in an already evil world are likely to be less severe than in one that isn't. Or perhaps resources are not used to track down criminals, but if criminals are found, their punishment is far more severe than is called for.

Short Lived

Unless you either have a campaign world with lower consequences for crimes or a campaign going for a payoff after lengthy investments of fairly low risk actions, it's very likely the campaign will be a short lived one because the characters will be. Dice rolls are bound to be low at one point or another, so when consequences are at a more realistic level, it likely means a character is bound to pay for their crimes. There are ways around this of course, simply being more lenient usually does the trick. But if this is not an option for whichever reason, make sure everybody in the group is aware both the campaign and their characters could come to an abrupt end when the dice rolls go awry.
Should this happen, the people responsible for the deaths of the player characters are likely celebrated as heroes in their world, which could make for a fun starting point of the next campaign should your players be willing to continue the stories of these NPCs.