A session of neurofeedback involves putting electrodes on the scalp to measure the brain electrical activity. The application of electrodes usually involves first cleaning dead skin off the target area. EEG paste adheres the electrodes (as in this picture) and makes a good electrical connection (although can be a little messy in the hair). Application usually takes only a few minutes, depending on how many areas of the brain are being targeted (and thus how many electrodes are used).
The real work of the session occurs while the trainee watches a computer monitor, sometimes playing a game or even watching a movie. What makes this specific training is the fact that the game or movie changes in some way based on the measured brain activity. If a certain type of desired brain activity is detected, it can be immediately encouraged by improving the gameplay or the movie quality - perhaps the rocket ship flies faster and the engine gets louder. Brainwaves are constantly changing, second by second, so there are dozens of opportunities every minute to teach the brain to operate in a different way - engaging in some types of activity more or engaging in other types less. Training usually lasts some set time between 10 minutes to an hour, depending on the type of training, the condition the trainee is in, and the habits of the trainer. Just as for a physical workout, more training isn't always better.