The government, entertainment and software industries have each put a lot of time and effort into combatting copyright infringement, including software piracy. So far, most of the public relations effort I've seen has been focused around either trying to shame people into not pirating software, or trying to scare people with the legal consequences of piracy.
So far, neither method has been effective. Shame is not effective because public opinion is that despite piracy, the victim corporations are still making tons of money. A combination of high prices, high corporate profits and the fact that corporations are faceless entities prevents people from empathising with their position. To date, fear has not been effective because the number of people sued or prosecuted for software piracy is incredibly low. People (correctly) see that they can get away with it as long as they're not major distributors. However, this viewpoint may change if law enforcement is able to exert more resources against software piracy.
Personally, I think a better approach would be to show people how they can be harmed by software piracy. Any time you place a program on your computer, you are entrusting your hardware and your data to not be abused by the program you're downloading. That's fine when it's a corporation providing you with the data because there are consequences (lawsuits, bad PR) if they provide malware in their software. However, you have no such guarantee when downloading software from warez websites or peer-to-peer applications like BitTorrent. Macs and even "jailbroken" iPhones have been virus infected by pirated software.
Pirating an OS is even worse, as a pirated OS is generally not eligable for security updates, leaving it vulnerable to hacking or virus infection. That is one likely reason that China has such a high proportion of hacked computers.
Although it's currently very unlikely that any given software pirate will be arrested, it's far more likely that their computer will be taken over and used for malicious purposes. I think if people were more aware of that fact, it might actually make a difference in the amount of software piracy.