QUESTION: How do I use dialogue to explain worldbuilding?
If you want to use dialogue, you can sprinkle the information through a series of scenes so the reader gradually gets the information.
The method most writers use is what I call "inform the outsider.” The outsider can be a newly turned vampire, the human love interest or ally, etc., and one of the vampires tells him/her about their history.
Or one character can disagree with another one's version of the story so they argue about it while informing the reader.
Or you could have one of the characters find a written history or story that's inserted into the story via dialogue. That's the most awkward method.
Or you can sprinkle in tiny bits of information in relation to what the characters are talking about so that the reader can add together the information to get the bigger picture. Having the reader figure it out himself is far more enjoyable to him than having an info dump.
One thing you need to consider is how important that element of worldbuilding is to the reader. You may have a clever new form of vampire, but unless the reader absolutely must know how that came about or the story won't make sense, the reader needn't be told all that information.