You have probably already heard this one but Diet is huge for ADHD and ADD. There may be diet triggers for the behavior that you don’t recognize. That is the first place to start.
It is also very important to remember that humans are not made to be attentive for long periods of time. In fact the brain quits actively learning after 20 minutes of inactivity. So every 20 minutes we need a “movement break” to get our brain back into an active state. Kids with ADHD need this even moreso. A kid with ADHD should have a chance to move around every 20 minutes, if this means getting a dr.s note and having the teachers involved then all the better, hard work but it is beneficial (at school it’s probably not likely to be able to move around every 20 minutes but you should find out how often the kid gets a chance to move around and increase that).
Along the same lines, these children need opportunity to engage in physical activities. And should be encouraged to do so daily. Even in the winter. They need to have something to do that occupies their bodies.
Also ADHD is a symptom of over-activity. So the advice above about removing TV and Video Games is very good advice. It doesn’t need to be removed completely but it does need to be drastically reduced.
Music is an effective calmer (and it doesn’t matter what type as long as it is soothing to the listener), so is circular motion such as swimming and biking. Massage is also helpful for relaxation. You can even teach self massage, such as rubbing ones feet when they start to feel anxious.
Another positive step is teaching the kid how to recognize changes in their behavior so they can begin to modulate it themselves. There are specific techniques for this. An easy one is to sit down with the kid. Then ask them to put themself in that “active” mood. Ask them to identify the mood on a scale of 1–10. Then ask them to increase it by a point or two (if they say they are 5, ask them to bring it up to a 7). After they increase you can practice having them try to decrease it (to a calmer state). This is a way to become aware of your mood and begin to have control over it. After doing this excercise a few times (and only after doing it and making it fun enough times the kid “gets it”) when the kid starts acting up you can ask them to try and identify their mood and then bring it down a notch. Eventually they should be able to do it on their own.