The term canon refers to everything that is created by either the original creator, or current head of the series, unless otherwise noted. This is the universal definition of what canon means. In Asia, and especially Japan however, concern over canon and non canon is not so much of an issue over there with their media creations. Akira Toriyama never specified what is canon or non canon, as it seemed like something he was not concerned with. Because of this fact, we are left to use, by default, the technical, universal definition of what canon is.
With that universal factual definition, in Dragonball's case, canon is everything that is in the manga created by Akira Toriyama. If it isn't in the manga it is non canon.
 Non Canon
The term non canon refers to two main things:
1. Anything that was not created by, not originally thought of by, or had very minimal involvement with Toriyama. (Unless otherwise specified)
2. Anything that is not in the manga.
The DB and DBZ movies and all of GT are examples of non canon. Although Toriyama helped a bit here and there on some of them, and even designed some of the characters (Broli for example), the original ideas for the movies were created by Toei, not by Toriyama. He had minimal involvement, and some of the movies he had zero involvement. Not only that, but the plots and settings of most of the movies contradict the series/manga timeline and events out right. The movies and GT do not have mangas.
Anime Filler in Dragonball and Dragonball Z is also non canon as most of it also either had minimal involvement from Toriyama, or none at all, and is not in the manga.
There are a couple of exceptions to these rules of canon and non canon. As stated earlier, unless otherwise specified, works for a series not created by the original creator or current rightful owner of the series are considered non canon. Toriyama did do this in one instance. Bardock was originally created by Toei for the Bardock special, a non canon telling of Gokus father's last days alive. Originally Toei created very different depictions of Bardock and his crew (Anyone have the picture?), but Toriyama came in and re-designed Bardock and his crew to the familiar faces we all know. Toriyama liked Bardock's character so much he put Bardock in a couple of panels in the manga, making his character canon. The Bardock special itself remains non canon over all.
The Trunks special is a canon special although created by Toei, the events of the Trunks special did happen in the manga. Toei basically followed the story of what happened in the manga, but put it in a special instead of a part of the series. They changed a few details around, such as when and how Trunks went SSJ, but for the most part sticked to the canon story.
The Trunks Special being canon is the same thing as the Toei animated anime being canon, minus filler and changed dialogue.