Detaching the braces from the teeth takes about a minute. Cleaning off the adhesive is done carefully and takes longer, and then the teeth are polished. We usually take final photographs to document the case and an impression of the teeth so that removable retainers can be made. If a fixed retainer is planned, it is made in advance and bonded at the same appointment. Every orthodontist takes a different amount of time over these steps, so I can only tell you how long they take me: removing the braces, taking the photographs and the impression takes around 40–50 minutes. Fitting a fixed retainer takes about 1 hour.
This answer is for general information. Your own case needs an examination by an orthodontist.