Double bridles are bridles with extra parts. They have two bits, extra cheek pieces and two pairs of reins. The double bridle is essentially made up of two different bridles, a snaffle bridle and a curb. On one of these bridles, the snaffle is called the Bridoon and the curb is generally a Weymouth.

Double bridles are usually found in dressage, only in levels elementary and up. You should only ever use a double bridle on your horse when they know how to work in a consistent, soft contact in a snaffle, as the extra bit on a double bridle is hardly used, only when needed and helps keep a soft connection with your horse, you still have your consistent contact with the Bridoon, where as you can let your Weymouth rein a little more loose. 

Although double bridles are mostly used in dressage, they are also legal in show jumping and cross country, for a little extra control over the horse. They can also be found in showing where more control over the horse is required. 

To fit a double bridle, it's mostly like fitting a normal snaffle bridle. You fit the Bridoon as you would with a snaffle bridle, and you fit the Weymouth like you would with a normal curb bridle, like a pellham for example, it's very important that the bits are the correct size in the horses mouth, as that's more metal in the horses mouth than normal, and you want to keep them comfortable.