This article explains how to watch the five Twilight films, based on the book series by Stephenie Meyer, in order. You don't have to worry about chronological order versus release order; in this case, they're the same.
How to Watch Twilight in Order!
There may be some confusion about the order of the Twilight films for a couple of reasons. First, the films aren't numbered, so it's hard to determine the order based on the titles alone. Some potential viewers may also be surprised to learn that there are five films for only four books.
The extra film came about because the filmmakers split the last book, Breaking Dawn, into two parts. They wanted to make sure that all relevant parts of the story could be included.
You should watch the series in the order they were released, which is the same order the books were released.