They could start by infiltrating human society at all levels. Vampires are intelligent and could use their charm and powers to gain influence in politics, business, and media. Once they have enough control in these areas, they can start to manipulate humans to their advantage. Also, they could target key military and security installations to disable any form of human resistance.
Well, vampires in Twilight fanfiction could take over the world in a rather insidious way. They could start by converting key individuals in important fields, such as scientists and inventors. By having vampires in these positions, they could control the development of new technologies, perhaps even creating ones that would give them more advantages over humans. They could also create false propaganda to make humans believe that vampires are their protectors or some kind of superior beings. Slowly but surely, they could gain more and more control until they are in charge of the entire world. And during this process, they would have to deal with any potential threats from werewolves or other supernatural creatures that might oppose their takeover.