In my honest opinion there are very few possibilities available to the government and/or media to prevent activities such as downloading music for free or sharing media with peers. These activities are difficult to regulate and monitor, making preventive measures a serious issue. It is impossible for the government or the media to monitor friends giving media to other friends in the privacy of their own homes. Although it may impossible for the government and the media to bring a complete halt to this type of activity, there are a few options available that could at least reduce the volume.
Since the major issue for the media is the loss of money, the best way to reduce activities such as media sharing and illegal downloading, would be to drastically increase the prices for their respective media. Increasing the price for music, movies, etc. would account for the inevitable loss of money that occurs from illegal downloads and file sharing. Although there is a very real threat of this backfiring completely, with people avoiding purchasing media altogether, it is highly unlikely as at least some portion of the population would still be willing to pay.
For the government, one way they can reduce these activities is to regulate web activity on a strict basis. They would need to be far more diligent about regulating IP addresses and protocols to insure that any illegal downloading or file sharing would be caught on to. This method would especially work for the government if they could prove that the fines associated with these activities were real threats, and not just silly myths, a belief that many people who engage in these activities hold. However, this method also contains a serious problem in that a proposal like this would need to be voted on, which may be difficult as it is a clear invasion of the privacy of internet users.
One final opportunity the government and media have to reduce this activity is to come up with a sort of incentive program to prevent people from wanting to give media away for free. If internet users had a legitimate reason to not give purchased media away for free to their peers, it may reduce the amount of illegal activity occurring. This method may be difficult, however, since monitoring who shares media and who doesn't is a difficult task in itself. Since this activity is on such a large scale, it is nearly impossible to monitor. I believe this would be the best method for the government/media to pursue as it is least likely to offend or anger internet users.
As I stated earlier, I believe that regulating or monitoring activities like this are impossible without creating tension between the different groups affected. The government should have no place in this type of activity at all, since it does not immediately affect them. The media, while affected, should in a sense, "get over it", because these activities will occur whether they like it or not.